"A woman is (or not long ago was) under serious consideration for this role, or at least was wanted. But the one I knew of was not a pop star or a musical theatre star. A more "prestige" female actor. "
I have always wanted to see Pink in this role; I think she would be wonderful. But now, I can't stop thinking about Tilda. I just want to see Tilda in every random role possible.
I think people are desperate for this due to the versatility of the show. Stunt casting in my opinion is a major draw to this show. (And I use stunt casting in a positive light, on the current Broadway run I don't think there has been a 'bad' Hedwig as such.)
The whole point of the show is to challenge gender and people's perceptions. What another great dynamic for the show to explore a Woman playing a Gay Man who has made themselves into a Female Rock Star!
What could be interesting is once the have explored this could they then find a trans-actress to tackle the role?
Gaga must have some raw ability, as she was accepted into CAP 21 when they were still operating as part of NYU. It doesn't necessarily mean that it's still there, or wouldn't still need some major refinement (as she did leave the program early), but at one point in her life somebody saw something in her.
Not that I necessarily am a champion for her to take on this role, but I wouldn't dismiss her as an actress immediately just because she's primarily known for her music and Gaga persona (which, in some ways, is a 24/7 acting gig, because Gaga is essentially a character that Stefanie Germanotta created and developed).