With a game whose history is as long as baseball's, it can be hard to nail down one single thing to change. After all, I have issues with baseball's finances, the fact that the All Star Game determines home field in the World Series, or how balls and strikes are called.
But to me, the designated hitter is the most eggregious of these things.
The problem is that it creates two different games in a single league. Imagine if, in football, teams in the NFC had a rule that the kicker kicked field goals, but was required to do the punts and kickoffs as well. Meanwhile, in the AFC teams could have a different guy doing kicking and punting, as it is now. Teams in the NFC would be at a disadvantage because their one guy has to do all the team's kicking while the AFC teams can have a specialist for each position.
This is what you have with the designated hitter. You have over-speciaization. Instead of baseball players, you have guys whose sole job it is to either hit or pitch.
I believe this leads to stagnation of teams as players who may have retired or been released when their skills diminished in the field extended their careers as designated hitters. Those spots in the lineup may have been filled by worthy, younger players.
Plus, you get pitchers who haven't swung a bat since high school. They are no longer baseball players if they don't take a plate appearance.
The fact that the NL and AL have different rules makes it a different game from one league the other, which is unheard of in major sports. No sport on earth has different rules for two leagues that compete against each other, except Major League Baseball.
I have two suggestions for this situation.
The first, again not my preference, would be to institute the DH in the national league. I don't like the DH, but at least then both leagues would be playing the same game.
My preference would be to abolish the DH. Make pitchers be baseball players again. Make them bat, the way the game was created and intended.
Whimsical change I would like to see: Let's start calling it the fair pole, instead of the foul pole. If the ball hits it, it is a fair ball. It should be called the fair pole.