When I was at BATB (for the first time) two weeks ago, there was a grandfather of a boy in the audience talking with a mother of two girls behind him.
He said that he took his boy to see BATB eight years ago as his first show. He went on to say that he can't behave in church, but in the theatre he sits and watches like a guard dog. Since, his son "dragged" him to Seussical, Phantom of the Opera, Lion King, and Tarzan. They were seeing Poppins the next day.
The woman said this was the girls first show and first time to New York. After the show, she asked the man about getting tickets to LION KING.
There is no question, for me, that Disney has brought families to the theatre that never would have gone otherwise. Whether it is the kids dragging the parents or the parents bringing the kids. It seems in the end -- all have been happy. I've never heard about kids/parents NOT liking it (although I am sure plenty haven't, I've never heard/seen this).
That being said, I think Disney recognizes this. They have a responsibility to bring a quality to their shows. Disney has mastered the spectacle element that makes kids (and their parents) go WOW! Now they need to work on their storytelling through their scripts.
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle