I know this is an older thread but this is a very good point and a similar situation exists for recording, overflow, BOH feeds, intercom program audio, etc. However, many theatres use a single ambient mic or a stereo pair of ambient mics rather than direct inputs or close miking for music. That way you get more of what the audience hears than just a dry signal.Also just thought of this - we have ADA Hearing Assisted transmitter/receivers. The hard of hearing will want to hear the music as well as the actors.
I don't think it was mentioned during the original discussion but your house system and how the levels from it and the natural sound from the pit vary over the listener area could be a factor. For example, if you put mics on some instruments but did not mic the brass then might you end up with a result that was brass heavy for some of the audience and brass deficient for others? Similarly, what about the balance between the orchestra and the vocals and might that vary? Its very hard to guess at such issues without knowing and having heard the space and system.