I don't understand the rationale for limiting the number of SUCCESSFUL challenges in any sport. Obviously, one can't permit an unlimited number of frivolous challenges. However, if, for example, two incorrect calls have been made and corrected, why should one lose the opportunity to rectify the next error(s) also? There have been many credible allegations that officials in baseball and hockey are biased for and against some players.
You have to limit them as in the NFL, otherwise the games will take 10 hours to play as challenge after challenge is issued. That is why the NFL imposed a limit, to force the challenges to be issued strategically and very judiciously and you lose a timeout if you are wrong. In baseball, they would have to impose a limit and exempt balls and strikes calls otherwise the games go from being 3 hours long to 6 hours long. It's really that simple.
In all likelihood, 2 challenges, maybe 3 at most are enough. Managers would be wise to: (1) save them if the game is not close at the time of the disputed play; (2) depending on the situation, in a close game, use them only when needed to overturn a blown call that costs you runs and potentially the game.
You can also discourage overuse of challenges by assessing a strike against the batter or a ball against the pitcher depending on which team loses the challenge. Or something like that. Imposing this kind of a rule change will make for interesting strategy in using or not using challenges. It will also create drama and entertainment and that is what the fan is paying for. What fan is not going to get a rush watching Lou Piniella run out of the dugout and throw a red flag at an umpire? I would pay to see that.
I think there are sufficient cameras and angles now for instant replay to be beneficial in baseball. Now and then you see a disputed play replayed and the replay is inconclusive, and if that is the case, you do exactly what the NFL does, you let the call on the field stand as there is no evidence to controvert it.