I have to say at the start that I think Bill Belichick is an a-hole.  But sometimes a-holes are right (personally, I count on it).  This is what Bill Belichick recently said about extra points and kickoffs:

Philosophically, plays that are non-plays shouldn't be in the game. I don't think it is good for the game. Extra points, when the odds are 99 percent range in extra points it is not a play. Let's move the ball back to the 15-20 yard line and not make it a tap in. Let them kick it. Same thing with the kickoff return, if you're just going to put the ball on the 20, put the ball on the 20.

Let's start with the extra point. 

Why is it there?  I think it is the appendix of American football.  It is a vestigial remnant of American football's father (or grandfather or great-uncle or something), rugby.  In rugby, after a "try" (analagous to a touchdown), the player that made the try, gets to attempt a "conversion" by making a moderately long kick from the point on the field along the line of where he went into the goal area (if he made the try by the sideline, the conversion kick is attempted from the sideline.  In short, the kick is made from a decent distance, from a potentially difficult angle by not necessarily the best kicker on the team.  In American football, this has been watered down to an extremely easy chip shot, attempted by a designated kicker who is about as much of a football player as your average sideline reporter.  As Belichick rightly pointed out, such kicks almost always succeed.  So why bother?  It seems to be an unusual, artificial construct which doesn't really add anything to the game.

So what should be done about it?  Axe the one-point conversion.  Belichick is in favor of a longer kick.  I don't know why kicking for an extra point should be a part of the game at all.  But I don't want to do away with conversions entirely.  I like the extra play for an extra point or two.  So put the ball on the 5-yard-line after every touchdown for a try at a 2-point conversion.  Two points is a big deal.  It's 1/3 of a touchdown.  So make it difficult.  Make it an exceptional play that is worthy of the points.  There's also the idea, mentioned in the above linked article, to make touchdowns 7 points, with the option to risk a point or gain a point by attempting a conversion.  If you make it, you get 8 points, if you don't, the touchdown is only 6 points.  I don't hate that idea, but I prefer the more traditional 2-point conversion from the 5.

Kickoffs are a bit more complicated.  Unlike the one-point conversion, kickoffs make sense.  While not necessary, one team giving the ball to the other to start play follows a certain internal logic ( See, for instance, baseball).  And I think they are fun and interesting plays.  But the NFL is worried abo injuries and that should be taken seriously.  Sports are fun and all, but if we need to tweak a sport's rules in order to protect players from serious injury, then we should.  But are kickoffs really that dangerous?  I have no numbeutrs here, so I could be way off base, but are there a lot of injuries on kickoffs?  Are there a lot of serious injuries?  It doesn't seem that way to me, but I'd be interested in seeing the data.

Regardless, the NFL has chosen an odd way to deal with the injury risk of kickoffs.  They moved the ball up to the 35-yard-line for kickoffs.  Years ago, they moved the ball back to the 30 because kickers had become so good that they were inducing too many touchbacks.  Now the NFL has moved it back because they want touchbacks.  There is no play in the game more boring than a kickoff touchback.  If kickoffs are too dangerous, then start every drive that would have started after a kickoff at the 20-yard-line. 

But again, I don't think such a radical rule change is necessary.  What is dangerous about the kickoff?  Is it the wedge?  A few years ago, they illegalized a wedge with more than 3 players.  They could do away with the wedge altogether.  Does the injury risk come from players being hit by players who have built up the momentum of running at full speed for 50 yards?  If so then you could move the 10 players from the kicking team further up the field with the kicker back at the 30.  My point is that there are other tweaks that can be made to save the kickoff return.  Maximizing touchbacks is not necessary and is definitely boring.