Broadway stars are not even known on Broadway. I doubt that more than one person in five encountered on 42nd Street would even recognize the name of Kelli O'Hara.
So upon reaching the age of about 40, the stars head for television to become publicly known. Audra joins a network TV medical series that's already been done 100 times. Kristin enlists in a supporting role for a shallow political drama. Sutton puts away in the closet two of her three threats seen to such advantage in Anything Goes and hits TV paydirt in a romantic comedy.
You can't blame them. At that age many of the juiciest roles in musicals become off limits, and the stars themselves may just not be thrilled by the eight shows a week grind. Thinking of Chenoweth in the wonderful role of Lily Garland in the wonderful screwball comedy Twentieth Century and her description of her life style in between performances as "living like a nun." They have to try to pave the way for future roles in films and on TV.
O'Hara is a little different in that she has said in a couple of interviews that at her present age she would no longer just do roles for fun, such as Pajama Game and Nice Work. She wanted the future shows that she was in to "contribute to a discussion" of important issues. In her current recurring TV role, which I've not seen, she plays an anti-bullying advocate. Perfect. Not so sure about Kiss Me, Kate, unless they shift the focus away from broad comedy.