The only chance the leagues have of being uniform is if the NL goes to the DH. It's simply impossible the DH will ever be removed from the AL. There are a number of reasons, most having to do with the players' union, which is more powerful than the commissioner or baseball itself. (That's why there is not and will never be a salary cap.)
Taking away the DH would mean one less starting job per team in the AL. This would result in one player per team losing his starting job, meaning less value, thus less salary for this "ninth" starting player. (Admittedly, this wouldn't happen right away because the player would already have a contract in place, but 5-10 years down the road after the non-DH rule was in effect, AL teams would only have to pay eight "starters" instead of nine.) The players' union would realize this and never allow this to happen.
Also, the DH rule lengthens players' careers. That is why older guys like Mike Piazza go over to the AL. If it weren't for the DH rule, his career might be over. His value would certainly be much less if he had to play the field; there may not even be a position he could play, at least with any consistancy. This is the #1 reason why the players' union would never allow the DH to be taken away.
Whether you agree with the players' union's motives or not, or think that it's bad for baseball, the facts are the facts. They have the power, they won't allow it, and it will never happen.
But, speaking in strictly baseball terms, why is having the pitcher bat preferred by some people? I don't really see the strategy of seeing the pitcher bunt every 2-3 innings. Okay, I understand there is strategy involved in whether you remove the pitcher and use a pinch hitter, etc., but don't tell me the pitcher contributes to the offense (as I've read some of you say here). I can (sort of) buy the strategy aspect of the non-DH argument, but the act of watching the pitcher bunt over a runner in the 2nd inning...well, that part of it sucks.
Some will say I'm not a purist, but it's my belief that when the game was originally invented, the pitcher was an "equal" batter to the other batters on the team. (Think of a Little League game, where the pitcher might also be the best hitter on a team. In THAT case, of course there's no need for a DH.) However, over time, in professional baseball, the pitcher became more of a "defensive specialist" to the point where his offensive abilities no longer mattered. I just don't believe the forefathers of the game realized to what extent this would happen.
In other words, I don't think the inventors of baseball had the pitcher bat to create these supposed "strategic" moments in the game; they had him bat because he was as good of a batter as any other player on the team.