Stephen Moffat can't write convincing female characters to save his life so as long as he's got the job, I can only imagine how awful a "female Doctor" would have been. Someone I think on Twitter said that the best thing would be to have him write all the scripts for the next series, sack him and then cast a woman in the role.
I don't "get" why more recently they've moved toward making the Doctor more sexy/sexual and relationships with companions have sexual undertones (or overtones) sometimes. The way Amy Pond and some of the other female characters were stylised in such a sexualised way was also pretty stunning.
It wasn't thus in the earlier days. I always thought David Tennant was just to pretty for the role. Even Peter Davidson struggled to hit that essential (quirkiness with a sinister edge) because he was too conventionally handsome, in my view. At least Matt Smith had that eccentric look and presence, but the scripts were just so crap that he seemed to just spend most of his time flailing his arms around. Peter Capaldi fits this mould and is a good actor, and is that bit older, but I predict the scripts will still be crap.
It's Sci-Fi and heaven knows enough so-called "rules" have been broken in recent series to try and give some plausibility to badly written story lines. If it were a historical piece, yes, you could argue against casting a woman or a person of colour as say Churchill or Henry VIII (not to say that it's impossible,) but with Dr Who, I disagree that there are such restrictions.
I heard Gene Roddenberry speak about 30 years ago about what he was up against, trying to cast actors of colour and women actors in the original Star Trek series and how how the story lines challenged the bigoted social conventions of the time in a subversive way. Nearly 50 years on, it's sad that Sci-Fi writers seem not to have that kind of courage interest in using the platform they have for social good.
I can't help thinking how wonderful it would have been to have Dr Who played by Pauline Black, or Tilda Swinton or Sophie Okonedo (yes, I know she was already in Dr Who, but so was Capaldi!) - all of whom could have done that quirky thing so well.
Have you seen some of the guff Neil Gaiman is spouting on Tumblr about why it's "not yet" time for a woman or person of colour to be cast as the Doctor? Gah!