Touchdowns are considered to be exciting, and the NFL has obviously done much tinkering with the rules over the past 40 years to enhance the scoring of touchdowns.
The NFL’s conventional wisdom, however, is that the kicking game is not as exciting, especially when you have a play which is as close to a lead-pipe cinch as the extra point has become.
I dont’ know if the NFL has ever narrowed the goal posts, but in in the 90’s the NCAA did narrow the posts to match the NFL width. And the NFL has moved the posts to the back of the end zone. (They were positioned on the goal line up until sometime in the early to mid 70’s.) And, as you pointed out, they have tinkered with width of the hash marks.
Originally in college football, (there was no NFL then), the ball was put in play from where the last play stopped. If this was a two yards from the sideline, then there might only be an end on one side of the center. I’m not sure if the center was ever on the end or not.
But the reason for gridiron was back when the forward pass was in its infancy, it could only be throw if the passing back was at least five yards to the right or left of the spot of the center snap. The lines going up and down the field were to help the referees judge this.
That being the case, why not just use only non broken-in balls thru the whole game, rather than just in kicking situations?
Likely because quarterbacks would complain (and, unlike kickers, star QBs hold no small amount of political power in the NFL). They would (possibly not even inaccurately) argue that “fresh” footballs would be more difficult for ball-handlers (QBs, RBs, receivers) to handle.
As I noted a couple of posts ago, the NFL is unlikely to make a change that negatively affects offense / the passing game.
I’m not sure how I feel about the change myself (my gut says they should just have made TDs 7 or 6+ an optional 2 Point Conversion but I don’t know) but in the NFL’s view, the fact that PATs where almost never missed means, to them, it was broke.
They did. Then in the mid-2000s Peyton Manning and Tom Brady successfully petitioned the league to allow teams to break in their own balls.
Presumably their argument was that it would help the offense to score points, which makes the game more exciting for fans.
IIRC, the change that was made at that point was allowing the road team to supply balls which had been broken in to their liking, for use when they were on offense. Previous to that, it was the home team’s responsibility to prep all of the balls for each game (for both teams to use on offense).
Before 2006, the home team provided all the balls, and they had to be new on game day. While they could try to break them in a little, there’s not much you can do in the morning before kickoff. Much like K balls now, which must be new on gameday but can be broken in for around 45 minutes before kickoff.
For example, the Giants equipment guys spend months prepping Eli’s footballs. (Link)
From the end of the linked article:
I like this idea, but do it even more rugby style and spot the ball in line with where the touchdown scoring player went down. E.g., for a run up the middle, the kicker can kick the extra point from the middle of the field. For a touchdown on a deep ball, the receiver has a chance to take a knee in the middle of the end zone to help out his kicker. But a touchdown scored in the corner of the end zone will force the conversion attempt from near the sideline. You can even let the kicking team spot the ball farther back than the 2 yard line if they’d prefer.
I do not know if it matters to anyone or not and I do not know if football’s scoring system was made to allow this but the scoring system as it stands allows for any point combination you can think of.
I am no mathematician but I would assume removing the extra point altogether would change that dynamic.
Is it an important dynamic? A curiosity? I dunno, just food for thought.
No it is impossible to score only a single point as you can’t score the extra point unless you make a touchdown first. In college you can score a single point if on an extra point attempt, you get what would normally be a safety. And in the CFL a single point, the rouge, is possible.
Just make the goal post a round circle of about 15ft diameter.
Now we’ll see how good the kickers are. 
The PAT has no impact on possible score totals; instead of a 6-point TD with a missed PAT, substitute two field goals for that same 6 points.
EDIT: And now that I see Beef’s idea isolated like that, it gives me a goofy idea:
Remove the kick entirely. Change touchdowns to be worth 7, and the extra point (worth only a single point) would be the same as a 2-point is now: ball at the 2, you must break the plane. Essentially, “going for two” is mandatory and is only worth 1 point, with the base touchdown worth 7.
I was saying that TDs would be worth 7, rather than 6, unless you specifically opted for the two point try, in which case they’d be worth 6 + 0/2. In other words basically just an automatic 1, if that’s what you wanted.
I would support your system, since I think scoring plays from the 2 yard line are pretty exciting and certainly more interesting than an extra point. It would also lead to tense situations where a team was up or down by 1.
Pretty much everything in this thread was preferable to the status quo.
NFL uses hashmarks that are the width of the goalposts (18 1/2 feet); NCAA uses 40-foot-wide hashmarks. High school uses 53 1/3-foot-wide hashmarks; I have seen fields with three pairs of hashmarks on them. The NFL moved them to their current positions in 1972.
That’s one of the ideas that I’ve seen discussed quite a bit as the PAT issue has been debated in the past few years, though the version I’ve generally seen is that going for two would take the “automatic” 1-point PAT off the board; if you missed the two-point attempt, you’d only get 6 total points, instead of 7.
(Edit: or, what SenorBeef described. 
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EXCEPT the stat for 33 yd field-goals made from the center of the field is around 95%.
That’s still one miss in 20, as opposed to three misses in a thousand.
I don’t understand what problem this is supposed to solve.
Don’t get me wrong, I know the numbers and know that PATs are almost never missed. But changing that presupposes that there is a problem.
What football allows for now, which I think is the point Ellis Dee misses, is that there is a strategic decision to be made; either take one point you are nearly certain to get, or attempt to get two points you are not certain to get. It offers a strategic decision that may come into significant play in some game contexts. It’s a good thing for the game. You could have essentially the same thing by just allowing a team to take a free point and not bother kicking the ball, but the idea of giving seven points and ALWAYS going for a eighth point by getting the ball in is pointless in that there is no strategy. The current system is basically “Take 7, or risk getting six in an attempt for eight.”
What will moving the PAT back accomplish? As near as I can tell, just two things:
2. It places more value on your kicker.
Are there any football fans who really, really want to see more emphasis on the KICKING game? Kickers are already the football players who aren’t really football players.