There is no reason they SHOULDN'T have it. Umpires should not be allowed to dictate and/or alter the outcome of a game by making incorrect decisions. Other than balls/strikes (which would be helpful to some umpires...since they can't figure out the strike zone), instant replay should be allowed. The game has lasted this long without instant replay, because it didn't exist until recently. It could be similar to football's approach, with each team being given 2 per game through innings 1-7, and only the replay official could make the decision to look at the tape in the last 2 innings. If the managers don't support instant replay, they don't have to challenge.
I disagree with just home runs and fair/foul because there are many other plays that impact a game. Not every run scored is due to home runs.
Quite honestly, the technology is so advanced that it is nearly impossible to make the wrong call in these situations with replay. It is a shame they would rather have the wrong call be made than to ruin the so called "purity" of the game. What is right may not be popular, but it is still the right thing to do.