Earlier quoted context omitted.
It's a little weird, especially since the musicians aren't visible to the audience - why would you play live?
People go to Broadway shows to see live performances, and music is a big part of it (in some shows, the biggest). You may say the audience won't know the difference. But word will get out. Audiences may not be willing to pay premium prices for prerecorded content.
Does the potential for failure and variation attract the audience? Or just the fact that the medium is much higher fidelity: stage actors are human, three dimensional, and no other medium can record all the subtleties of motion and expression just as well.