The more “points” needed to win a match, the less likely it is that the lesser skilled opponent will get lucky and win. That’s the bottom line.
Two years ago the Seattle Mariners went 116-46 in 162 games. They tied the record for the most number of wins ever in a regular season with the 1908 Chicago Cubs. This is your benchmark for determining the very best team: 71.60% winning percentage.
The record for number of losses in the regular season is 120 for the Nuh Ymmk mumblemumble. This is your benchmark for losing teams: 74.07% losing percentage.
However, the playoffs are not a competition between these two radically different teams, are they? The 2001 Seattle Mariners will never play the 1962 Nuh Ymmk mumblemumbles: instead, the 71% winning Mariners played the Cleveland Indians (who probably had a winning percentage of about 60% or so). They obviously can’t each win their respective percentages, because they both can’t win the series, so the longer series allows for narrow differences to play out effectively over time. Otherwise it’s Your Best Pitcher against Our Best Pitcher.
A three-game playoff would probably be one home, one away, one home (or vice-versa). There would likely be travel days in between (as there are travel days now, when the players switch venues). In this three-game series, Randy Johnson could pitch game 1, travel, rest, travel, and pitch game 3 on three days’ rest. That series is weighted toward whichever team has the best ace pitcher; the game 2 starter means nothing at all.
A five-game series is almost too short for this reason. You see a lot more of the aces than in a seven-game series. It gives the wildcards a chance they may not normally get over a seven-game series. It allows the wild cards to beat better teams in the first round, only to be blown away by the deeper pitching staffs in the second round. For this reason, a three-game series probably wouldn’t result in having the best teams in the playoffs each year.
Now we have to ask if that’s a good thing or not. 
FISH
Instead of arguing the point, I worked out the exact odds if two teams play each other and one has a 60% chance of winning any given game. In a one game series, of course, their odds of winning are 60%. In a three game series, it rises to 64.8%. In a five game series it is 68.256% and in a seven game series it is 71.0208%. This is elementary probablility theory (not statistics at all). BTW, it is utterly irrelevant whether they play out the rest of the series after it has been decided, as a half second reflection will show.
As the length of the series approaches infinity, the probability approaches 1, as should also be obvious.
I have to say that I watched nearly every minute of the LCSs, but cannot be interested in which of the Yankees and Marlins win and will sample it only. A Red Sox-Cubs series, on the other hand, ah the very ambrosia of baseball, tempered only by not wanting either to lose.
I hate to second guess managers, BTW, but at the end of the 7th inning, I predicted to my wife that Pedro was finished. He was shaky then, but got out of it. Maybe if the manager had seen it that way…