I am NOT a fan of live recordings.
The performances on stage usually don't come across well in live albums, and most theatres are not acoustically "tuned" to give live recordings the sound they need...lyrics are lost and audience noises are distracting. (A digital watch going off just before Barbara Cook sails into the first line of "Losing My Mind" on RCA's FOLLIES IN CONCERT album has always taken me out of the moment.)
Editing would be a problem. How do you correct one note or phrase from two different live recordings? Also some numbers are way too long on stage and need to be abridged.
In a proper recording studio the singers and orchestra can be adjusted, tempos can be modified, and the performers can tone down performances when not having to shout lines to reach the back of the balcony.
Financially, I doubt there is much to gain from a live recording as the cast and orchestra would still have to be paid their full fees (one weeks salary) and all other fees associated with making cast albums (to orchestrators, copyists, etc.) would still apply.
Cast albums are NOT "soundtracks."
Live theatre does not use a "soundtrack." If it did, it wouldn't be live theatre!
I host a weekly one-hour radio program featuring cast album selections as well as songs by cabaret, jazz and theatre artists. The program, FRONT ROW CENTRE is heard Sundays 9 to 10 am and also Saturdays from 8 to 9 am (eastern times) on www.proudfm.com