One thing I would like to see MLB do is allow the home team, regardless of league, decide if each game is played with or without a DH. The concept is pretty simple: Before each game, the home team's manager gets to declare if they want to play with or without a DH that day, and whatever they decide, both teams play under that rules package. (To give the other team fair warning, there would be a designated amount of time before first pitch - let's say three or four hours - that the home team has to lock in their decision. They don't have to post the lineup itself by that time, but they have to declare which set of rules they want.)
This simple change would have several positive impacts:
1) It would unite the two leagues under the same set of rules, which seems like a good idea since there's now at least one interleague series ongoing all season, every season.
2) It doesn't fully kill either style of play. There will still be games with the DH, and there will still be games where the pitchers have to hit.
3) It will strike a good balance by allowing aging players to still use the DH to prolong their career, but at the same time, it won't allow dominant hitters to play every game without owning a glove. The system will always check and balance itself.
4) It will add a tremendous strategy element that each manager will have to juggle while simultaneously promoting baseball discussion every afternoon in cities across North America circulating around what set of rules the hometown team should use for that particular game.
5) It will provide the home team with a little extra advantage, which I think is a good thing since MLB tends to have a smaller home field advantage than pretty much any other major team sport.
More often than not, I think teams would use the DH, but there's several instances where I could see them changing course. They include, but are not limited to ...
A) They have a pitcher that hits much better than the opposing pitcher. They don't even have to be a great hitter in general. Just enough to give the team a distinct batting advantage at that position.
B) If the other team has a great hitter who is also a terrible fielder. In this case, they can force them to pick up a glove if they want in the lineup and see if they make a mistake on that side of the ball.
C) If the other team has a star player who is nursing a nagging injury. You could effectively limit them to pinch hitting for that game if the opposing manager doesn't want them in the field for nine innings.
D) If your bench is deeper than your opponent's. Since there tends to be more pinch hitters when the pitcher hits, the team with the deeper bench often has the advantage. Some managers might want to expose that against certain opponents.
E) If your starter is likely to be out of the game before the opponent's starter. In this case, you can probably buy your team an extra at bat with a position player since you will be going to your bullpen first anyway.
F) If your typical DH needs a day off or is a terrible match up against the opponent's starter. Suppose you're facing a really tough lefty and the guy you usually use at DH is a lefty that mashes righties. Meanwhile, you're also throwing a lefty that day, but your opponent has a righty they often DH that kills lefties. In this case, you can eliminate that advantage by taking away the DH and force both pitchers to hit. Then when the right spot comes up, you can use your big left handed bat to pinch hit in a high leverage situation against somebody from the opponent's bullpen.
For my money, this would be the best way to unite the two leagues under the same set of rules without destroying either style of play.