Laura Helmuth thinks it should be important even to those who don’t care about the show:
A female Doctor would go a long way toward making up for the show’s recent regression into tiresome
stereotyped sex roles.
The Doctor travels with human companions, usually one lovely young woman at a time.
As Ted Kissell writes at the Atlantic, the recent companions have been weaker and younger than the ones who accompanied the earlier Doctors.
Has Helmuth been watching the same show I have? Is Clara supposed to be weak? The woman in the photo, by the way, is the first female Time Lord in the series, Romana, in her first incarnation. Even the Times of London has weighed in:
The shift from male to female authority is difficult in politics and business but it is surely not beyond the capacity of the Doctor.
I’m cool as long as she isn’t called a Time Lady. And especially if they snag Helen Mirren. Alyssa Rosenberg argues a gender change is what the Doctor would want:
Wouldn’t he be curious, after all this time, to wonder what it’s like to occupy a woman’s body and to see what it’s like to live with a different set of gender roles (really, many different sets of gender roles)? Aren’t there some circumstances and societies where it might be more advantageous for the Doctor to be female or non-white? If the doctor was set up as an explicit exploration of masculinity, cycling him through all kinds of men’s bodies would make more sense, though it wouldn’t explain the Doctor’s continuing whiteness. But it’s not. And keeping the Doctor white and male over and over again is a contradiction to the show’s sense of wonder and exploration.
The Dish 