Sounds like making excuses to me. "Oh a female doctor could be ok" but then looking for reasons to decide it wouldn't work. The writing would be awful, they'll case an unsuitable actress etc etc.
Sexist or change-fearing attitudes in fandom need shaking up and our tragic, engimatic world-breaking travelling wizard can work as a woman just as well a guy.
Sure, but if they're casting a woman in a role that has been defined by (mostly) traditionally male traits, they have to at least think about what it means for the character. Is it asking for too much? Don't you think that the producers would think about that kind of thing, if they ever made a Mary Poppins
remake starring Rik Mayall as Mary?