I enjoy the stage performances - and even though the "Princess Dancers" (and their equivalents) have become a bit homogenous/a bit corporate - I still get a kick out of live acts. I don't think I'd be willing to pay extra for it - but I wonder if the cruise lines are missing a trick by not providing "back stage access" to the performing troupes? Maybe a few "first come first served" cocktail gatherings with the "stars?" Maybe a few "behind the scenes" get togethers with the performing artists?
Since a lot of them do double duty on cruises and work the bars and lounges, my son has met many of them during a cruise and loves hearing their various "port" tips...
I have taken such tours on several ships & there was no extra charge involved.
Carnival used to have a free "meet the cast" tour, now you can buy the "behind the fun tour" and meet one or two of them. We have been lucky, like Debbie"s son and met some of them on shore tours and/or places around the ship. Another way to interact with some of them is take one of the dance classes (usually free). All that said, I like your idea.
We enjoy the shows, I have taken several behind the scenes tours. I am amazed they don't come back onstage bloodied during their quick changing, not a lot of room backstage.