The problem with using recordings is that the musicians normally synchronise themselves and follow cues from the stage.
This is the biggest issue for me. Most of my pit experience is from playing musicals, and while everything you said applies, there's another issue - when one of the performers has a brain fart and skips the first verse of a song, a real pit orchestra responds instantly and seamlessly because they're listening to what's going on independently of the conductor, and know the show. If an actor misses a cue, the orchestra vamps until he gets his act together, and can make it sound like nothing out of the ordinary happened. If for some reason the conductor gets out of sync with what's happening on stage, the orchestra knows to ignore him and to follow the stage when need be. All of those situations have happened to me personally, and I've yet to see an electronic performance that can deal with them effectively.
Having said that, I agree with some of the other posters that most of the sampled/recorded music in musical theater today is there because of money. It's not cheap to field even a small (5-7 members) pit orchestra for a show that does even only five performances per week. It's been years since I had the opportunity to play a show simply because all the theaters around where I live don't use live music anymore.