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Some houses require at least one "live" instrument to perform their shows. Tams-Witmark has it right in the signed agreement. 

The first time I experianced recorded music to reinforce a small 5 piece band to sound like a 21 piece orchestra. Was when I worked on 'Disney on parade'. Which was performed in a big top through out Oz.
The music was on reel to reel tape, which was played in sterio & a metronome was superimposed on part of the tape. {How was achieved I'm not sure as it was all just about valves, wire & sticky tape in those days}
But the conductor only could hear the metronome beat in one ear & the taped music in the other, while wearing cans. I suppose this was a way of ensure the band was in the same beat & tempo with the orchestra, just in case the taped stretched with the heat in the Big Chapoe.
I was on a 'Lime' within a few feet of the canvas roof & I was being stretched, must have lost 10 litres of sweat per show. The pulpit was slung on to one of the tent poles, I sweated virtualy a puddle of water. Tended to worry as some of the punters underneath  looked up with a worried vacant look checking for rain.  [At least I think they hoped it was rain & not something else?]
But the funniest was a show back in the 60's called 'Instant Marrage' writen by some bod localy. Which we did with taped music for the first time. It was in the midle of summer  & it  must have been 140 in the water bag, for most of the season. The bio box was in a very small room with no ventilation under  a tin roof, which was part of the roof viod. I was actualy performing song & dance in those days. Nearly every time I was in the middle of a particular lovvie dovvie wobble, the tape would stretch & the girl I was singing it to would always start the giggles. Which in turn would get the punters cackling, at the my strangle mouth movements trying to match  the song to the music. Naturaly being a trouper I caried on regardless. At least untill I couldn't hold it in any longer, so I relieved my self by  going up! [As one does of course]
Thank gawd for CD's & I don't tread the boards any longer.
The beauty of your own software & midi set up, is with shows which have dialogue dispersed with the vocals/music. Is it can be split on to seperate tracks, so the techie on the music cue can switch to the next track, after the dialogue. I think we had 5 such cues & used 11 or so seperate tracks for one song. 

Realtime Music Solutions works with RnH Theatricals (who hold the rights for K&I) and MTI.  Their Sinfonia software is marketed as AccompanEase with RnH and as OrchExtra with MTI.  You must have contracted for the given show, in this case K&I with RnH Theatricals to be able to use (legally) the Sinfonia system.  RnH in fact was promoting it in their newsletter, Happy Talk, in January or February 2007.  Sinfonia is not just the music with the vocal tract cut out, it is each single instrumental part programmed to play.  If you have an accompanist, a bass, and a flute live (not that anyone would have that combination, but this is for example only so bear with me), you can silence those voices in the software and just have it play the rest of the orchestral parts.  The person on the midi can control tempo, transpositions, cut and paste for realtime errors...essentially they can follow anything that the conductor instructs.  If a singer skips a verse you can insta-vamp and then pick up at whatever measure the conductor instructs.  Repeats, holds...you name it.  We used it without any live musicians.  My sound guy programmed the show and set our parameters (just personalizing the tempos and pauses, minimizing the incidental music for set changes) and "ran" the show from the sound table, adjusting the orchestration as needed for the the actors daily re-interpretation of tempo (yes that was a little sarcastic, we had some timing issues..is 4/4 really so hard...)  My biggest piece(s) of advice:  know all the don't from the operation manuel, KNOW HOW TO RUN THE SHOW FROM THE LAPTOP FUNCTION KEYS AS WELL AS THE MIDI KEYBOARD (it saved our rear when we accidentaly did a "don't ever do this" on opening nite), and finally, have someone with musical experience run the software - it will save you hours of frustration.  I tried to run it, but it would have taken me days to get the gist of it. Its hard if you aren't familiar with musical notation (the software is programmed straight from the full score, but with no personal nuance)  But for even an amatuer musician its a piece of cake.  It was great, a little spendy, easy, and legal.

As I understand it - and this is only hearsay on my part - those software programs that are supposed to remove the vocals only do a partial job - in that certain frequencies are blocked.  BUT in so doing, you lose some of the music too which might occupy some of those same frequencies.  PART of the problem lies in the fact that on CD's, records or tapes, the individual studio channels or tracks have been mixed down to a couple of tracks (stereo tracks or such) and therefore in trying to remove certain VOICE frequencies you're bound to lose a lot of music too. PLUS the fact that from what I understand, it's never totally removed from a CD, tape or recording and never can be...just mainly minimized a lot at the expense of much of the fidelity and the music itself.  Now then on the software and tracks the companies are creating they CAN keep the tracks separated and thus you're able to remove effectively anything you want to have played LIVE.  BECAUSE they're computerized and that's the only place you can remove any individual tracks unless they have a TAPE system with multiple individual tracks that can be muted.  BUT the tracks MUST be created where you can do that and most CD's, tapes or recordings that can't happen because of having been mixed down to a couple of stereo tracks.