I don't think high frame rates are the problem. Quite a few old console games ran at 60 FPS, and a lot of newer games don't because the "realistic" graphics take too much time. Higher FPS are useful because they cut down on latency, so if a game requires quick reactions (e.g. a fighting game) high FPS are a must.

I remember reading that a lot of Counterstrike players turn down the visual details in favor of higher frame rate, since the visual details do nothing for gameplay whereas the higher FPS does.