Just a WAG: Team sports, as a broad concept, in Europe evolved from soccer, where ties are common, but in America they derive from baseball, where they don’t occur. The “natural evolution” from a listing of wins and losses is wins, losses, and ties, even though a sequence of very good, still good, and not good makes more sense.
Fair point, and I plead it being late when I posted that, and forgot that possibility. 
It does mean that both wild card teams would have to win on the road twice, likely at least once against a team with a better record, in order to get to that point. Improbable (since there have been wild card teams which have made it to the Super Bowl), but not impossible.
This is basically it: Baseball was the first major team sport in the US and established the order. College football added ties, but they were relatively rare, so no one thought to put it in the middle. By the time hockey came along (the first American sport* where you had a reasonable number of ties), people were used to it.
*Yes, it originated in Canada, but it wasn’t noticed in the US until the Bruins and Americans started playing. The Americans played in New York, which meant they had higher visibility. Still, most of the country knew nothing about hockey at that point. But it made sense for the newspapers to go W-L-T since people were so used to seeing W-L in the scores.
I’m mystified what American sports the OP could have been watching without seeing and hearing frequent references to playoff/postseason positioning. NFL broadcasts increasingly as the season goes on feature discussion of how Team X’s chances of going to the playoffs will be affected by the current game, whether it could get home-field advantage, potential opponents etc.
Yes, we tend to have few fewer of those scintillating 0-0 or 1-1 draws, and then only in soccer games and the rare NFL contest that ends in an overtime tie.
It must’ve been especially disconcerting to griffin1977 to experience actual game clocks showing how much time was left, instead of depending on a referee’s semi-arbitrary determination of when stoppage time, um, stopped. 
Teams have made it from the wild card and won it from the sixth seed. Steelers did it in Super Bowl XL. Packers then did it to beat the Steelers in Super Bowl XLV. Giants won from the fifth seed in Super Bowl XLII. Those are the last three examples off the top of my head.
In American football, ties are so rare they’re practically an afterthought so are tacked on to the end. And often omitted entirely; you know a 4-2 team had four wins and two losses. Even when comparing records where one team has a tie in their record and the other doesn’t you’ll sometimes see something like “3-5 vs 2-5-1”.
In a sport like soccer/association football, ties are not uncommon at all, so it makes sense to put ties between wins and losses when listing records.
Wonder if maybe there is a difference in American vs. European sports culture whereby American culture demands decisive outcomes (want one team to win and one to lose) whereas Europeans are more comfortable with draws/ties/stalemates.
You may be familiar with the cliche, “a tie is like kissing your sister.” (Which, AFAICT, has been attributed to every college football coach ever.)
In 1966, top ranked Notre Dame played #2 ranked Michigan state in both teams’ final regular season game. As the game neared conclusion with the teams tied, Notre Dame chose to run the clock out (and end the season undefeated) rather taking a more aggressive strategy and risk losing. Sportswriter Dan Jenkins bitterly wrote that Notre Dame had chosen to “tie one for the Gipper.”
US FB and BB don’t have a real minor league to use for relegation. Baseball and the NHL do have real minor leagues but the gap in money, talent, etc. is just too great between those lower level leagues and the major leagues.
And, a significant proportion of the minor leagues in those sports (particularly the highest levels of the minors) serve as farm teams / developmental teams for the MLB and NHL teams.
It’s discussed quite regularly. You’re just not paying attention.
But, to be fair, it’s not as important. In the Champions’ League, for example, the top two teams in each four-team group advance to the knockout stages. They only play 6 games (home-and-away round robin), so each game has a significant effect on the standings in the group and the ability to qualify out. And, they only play teams within the group.
In the NFL, by contrast, each “division” is a four team group, but they play 16 games, of which 6 are home-and-away round robin games, but the rest are spread out among the rest of the NFL. Only the first-place team is guaranteed a playoff spot; when sorting out what other teams qualify for the playoffs, conference standing rather than division (group) standing matters. So it’s not like it matters much on Week 6 that, say, Chicago is second in the North Division of the NFC, two games behind the Packers, since there will still be 10 games left to play, and the only place that really matters is first.
In short: unlike most soccer leagues and contests, position in the “table” isn’t that important, if it’s not first place in a division/conference. As the season wears on, it will quickly become clear who is still in the running for a playoff spot and who is not. If in Major League Baseball, the Yankees are 7 games out of first place in their division at the start of June, no one really cares much. The same thing at the start of September will cause some considerable muttering on the streets of the Bronx. :dubious:
To the point where there are contracts between the teams, at least in baseball. The minor league teams are individually owned but the player salaries (which generally aren’t very much) are paid by the major league club. Going to a game can still be a good time, but even AAA ball isn’t as good as the worst of the majors. And I’m someone who has seen lots and lots of AAA ball over the years, to the point where I go to Isotopes games wearing my one of my old Dukes promotional hats to the game. (It has ads for a supermarket chain that doesn’t exist anymore and a radio station that no longer carries the games printed on the back). It’s harder these days to care as I’m not a child (when these sorts of things are a matter of life and death) and the team keeps changing its affiliation. Plus the changes in the PCL and consolidation to two AAA leagues means teams that either no longer exist (Calgary Cannons, Edmonton Trappers, and Colorado Springs Sky Sox all spring to mind) or lots of teams further east that I’d never heard of. But the affiliation with the LA Dodgers from when I was a boy is why I’m a Dodgers fan today. Some players I either remember seeing or know I must have seen even if I don’t remember (with some assistance from Wikipedia) were Mike Piazza (I used to even have a promotional VHS that was mostly about catching that was made after he made the majors), Pedro Martinez, Paul Konerko, Eric Karros (who I think is doing some broadcasting these days), Raul Mondesi (who’s currently in prison in the Dominican Republic for corruption during his time as the mayor of San Cristobal), Jose Offerman (he committed so many throwing errors from shortstop but man was he fast), Todd Hollandsworth, and Chan Ho Park.
Just to expand on this a little, for the OP:
The NFL has 32 teams. The league is divided into two conferences, as noted earlier: the National Football Conference (the NFC), and the American Football Conference (the NFC), each of which has 16 teams.
Within each conference of 16 teams, there are then four divisions: North, South, East, and West; each division has four teams in it.
And, as others have noted, the “division” terminology may lead one astray, if one thinks of how European football divisions are set up. In the NFL, all eight divisions (and, thus, both conferences) are considered to be on equal footing, as far as organization and level of play.
So, continuing DSYoungEsq’s example, the North Division of the National Football Conference (nearly always referred to as “the NFC North”) consists of the Chicago Bears, the Detroit Lions, the Green Bay Packers, and the Minnesota Vikings. The current division alignment was established in 2002, and, generally speaking, most teams are in a division which makes sense for their home city’s location, and places them (relatively) close geographically to the other teams in their division. (The few examples where this isn’t the case – like the Dallas Cowboys being in the NFC East, are because of an attempt to preserve old rivalries which predated the current alignment.)
As DSYoungEsq notes, an NFL team plays two games per season (one at home, and one away) against each of the other three teams in its division (for six total games, out of the 16 on the schedule). This familiarity, as well as the fact that these four teams are all competing with one another for the division title (and the associated playoff berth) each season, typically mean that any given team’s biggest rivalries will tend to be against one or more of its division-mates.
Of the remaining 10 games on an NFL team’s schedule:
- Four games (two at home, two away) are played against the four teams in one of the other three divisions within the team’s conference; this rotates on a three-year schedule. For this past season, NFC North teams played against NFC West teams.
- Two games (one at home, one away) are played against teams in the remaining two divisions in the team’s conference, which finished the previous season with the same ranking in their own divisions as the team did. So, for this past season, the Packers (who finished third in the NFC North in 2017) played against the Atlanta Falcons (who had finished third in the NFC South) and the Washington Redskins (who had finished third in the NFC East).
- Four games (two at home, two away) are played against the four teams in one division of the other conference; this rotates on a four-year schedule. For this past season, the NFC North played against AFC East teams.
The net of this is, for any given team, is this:
- You see your divisional rivals a lot, because you play each of them twice a year.
- For any given team in another division in your conference, you play them at least once every three years, and potentially a bit more often.
- For any given team in the other conference, you only play them once every four years.
You do get an award for having the best record in the MLS but it doesn’t mean much*. It’s called the Supporter’s Shield. The reason they have it is because of how European (and other) soccer leagues award their championships for having the best record.
Interestingly, the MLS wanted nothing to do with it. It started from a grass-roots effort that raised money.
*Within the league itself, but the winner gets a slot in the CONCACAF Champions League.
In both places results are listed in order of preference. 
The talent level would even out enough over time. The real problem is the facilities. A single A baseball club is going to need a bigger stadium if they find themselves promoted to the majors. The 3,000 seat ballpark ain’t gonna cut it anymore.
Or, we’re using different words to discuss it than you’re expecting.
We’re less interested in placement among the rest of the teams than we are playoff positioning.
If you’re not getting to the playoffs, you’re lumped into the “no playoff” group, without relegation, there’s little interest in whether or not you’re a few wins ahead or behind another no playoff team.
If you are (or may be) in the playoffs, that is what gets discussed. Are you definitely in, are you not yet eliminated, can you secure a first round bye, or home field advantage? We also get the “Team can get into the playoffs if they beat X and Y, but they also need Z to beat Q or they’re out.” discussions.
There is rather a lot of prestige in winning the Super Bowl, and winning your division makes it likelier that you will do that. Anything that makes that likelier is a prize.
The home field advantage in the NFL is approximately five percent. That may not sound like a lot but it’s quite significant. Wild card teams simply aren’t very likely to win it all; only six have, in something like 40 years of this playoff system.
Perhaps the most significant advantage, though, is conferred upon the two division champions who finish first and second in the conference and thus get a first round bye. The advantages of two weeks off and only having to win three games instead of four are truly massive.
As to the OP, it depends on the sport. This time of year NFL fans are VERY aware of the standings (not “league table”) because every games in the last few weeks has huge implications. Fans of basketball and hockey are less attentive right now because
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We’re too early in those seasons to get really worked up about it, and
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They work differently.
In the NBA, 15 teams in each conference fight for eight playoff spots ranked one to eight. Consequently, most of the 15 teams, even at the end of the season, will either be very clearly in the playoffs or very clearly out. Even now, if you look at the Eastern standings, it is essentially certain that Milwaukee, Toronto, Indiana, Boston and Philadelphia will make the playoffs, and equally certain that Cleveland, Chicago, New York and Atlanta won’t; only five or six teams could go either way and by season’s end a few of those will be on one side or the other of that line. Fans of teams clearly in or clearly out can’t get really worked up about it - unlike a promotion/relegation system where it matters in TWO places on the standings.
In hockey, the playoff system is, to be honest, much more weirdly complex than it needs to be and there’s not a lot of point worrying about it until close to season’s end.
Baseball isn’t being talked about now because it’s January, but the standings are REALLY important; it allows fewer teams into the playoffs than the other leagues, and four of the ten spots only entitle your team to a one game playoff for the right to get into the real playoffs. I assure you that baseball fans are keenly aware of their team’s position in the standings; baseball is played more or less every day so it can change every night.
The NHL has a similar award, the President’s Trophy.
Yes and no. Division standing does matter in one sense. When deciding who qualifies as a wild card team in the playoffs you often have teams with tied records. To resolve that conflict you first determine whether those teams played each other and who won; the winner of that game owns the tiebreaker. If that doesn’t resolve the tie then you determine which team has a better division record (who won more games against teams in their own division), and then that team owns the tiebreaker. So in a sense, division standing somewhat matters beyond being the division champion; or at least your division record matters.