I've said this before - but I think there needs to be a distinction between STUNT casting and STAR casting. Stunt casting would be a fine term for bringing in someone of a huge magnitude who really is there to sell tickets, but isn't right for the role.
When the celebrity is great and appropriate for a role, has more of theater background (as in this case) and just "happens to be" famous, it's STAR casting.
Whether Anneliese was on TV or not, she's a fiercely talented actress is deserves to be up on that stage. And believe me, she went through a vigorous audition process, just like any other performer. She wasn't handed the role by any stretch.
All that being said - am I the only one that hears an amazing likeness to Judy Garland on that very last clip?
"A little nonsense now and then is relished by the wisest men" - Willy Wonka