David Pogue, who knows a thing or two about orchestral music, says that his son is "absolutely right" in averring that, at the Rockettes Christmas show at least, a taped orchestra sounds better than a live one. I suspect he's right. The orchestras at Broadway musicals and Radio City spectaculars are union shops, who hack their way through tired scores at scale and are rarely if ever appreciated by the audience. The advantage of a live orchestra is not so much auditory as strategic: if a Rockette falls over halfway through a routine, a conductor can react a much faster and more sophisticated way than a tape operator who's going to find it hard to start up again from Bar 97. More subtly, the conductor can adjust the pace of the music according to how the Rockettes are performing that night.
In fact, this is the reason most often given for why ballet orchestras are so much worse than opera orchestras. The primary responsibiility of a ballet orchestra, we're told, is to keep up with the dancers, which might mean changes in tempo that no conductor would ever impose by choice. But the real reason, I suspect, is that the audience at the ballet is much like the audience at Spamalot: they really don't care that live musicians are playing, and it doesn't affect their enjoyment of the show one whit if they're not. And no musician can keep on playing to a first-class standard if no one really cares how they're doing.
Most demoralizingly of all, orchestras on Broadway and at Radio City are amplified, which means that you lose nearly all the sonic advantages of live players right there. In fact, it's probably time to realise that most Broadway orchestras are tired anachronisms which owe their existence wholly to their union, and that they have been ever since the age of universal amplification began. Maybe if they were abolished, we wouldn't have abominations like amplified opera.