IIRC, back during the Pierce Brosnan era, they talked about doing a female spin-off film, focusing on either Halle Berry's character from
Die Another Day or Michelle Yeoh's character from
Tomorrow Never Dies. While Berry really sucked, I was always bummed that we never got to see Yeoh again.

(I also heard rumors that Berry's role in
Die Another Day was originally going to be a return of Yeoh's character. But sadly, that never happened either.)
Frankly, I don't think too many people watch
007 movies for progressive gender roles. The very purpose of the franchise is unrepentant machismo. If they can work in some strong female characters at the same time, that's fine but it's not essential.
Complaining about there not being enough strong female heroes in a James Bond movie is kinda like complaining that there aren't enough explosions in a Jane Austen novel or that there aren't enough white people in Tyler Perry's movies. Not everything needs to be a pantheon of diversity. Not everyone needs to be represented in everything. Some things should just do what they do.
And if you wanna see kickass lady action heroes, I recommend the
Resident Evil, Underworld, &
Tomb Raider series.
(Meanwhile, my main complaint about the Daniel Craig movies is that he just doesn't seem to be having any fun while doing them and completely lacks the suave charm that all of his predecessors had.)
I don't want them to do it just because they can, or just to tick a box, but if someone is perfect to play the Doctor they should get the chance, whether they're male, female or...and I appreciate this may be a step too far...American!
As an American myself, I say that's blasphemy!
And speaking of Agent Carter, I just saw something about a Twitter campaign to make Captain America gay. *sigh.....*
Would they be happy if Marvel created them a gay or bisexual hero instead?
Would RTD loan Disney the rights to Captain Jack for a few movies?
Thanks to
Pirates of the Caribbean, Disney already has its own Captain Jack!
As for making Captain America gay, that's ridiculous and already contradicts his established relationships with Peggy & Sharon in the previous movies. If you're that interested, I'm sure there's a wide variety of Cap/Bucky slash fanfic out there.
Meanwhile, I just want to say again that I miss
Agent Carter.
As for getting this thread back on topic, or at least back in a
Doctor Who direction, I'd be OK with a female Doctor so long as it didn't substantially change the character. The wise, eccentric, distracted scientist is the essential archetype for the character. Traditionally, that's been a male archetype, albeit a non-sexualized one. But so long as a woman can fit that non-sexualized archetype, I'm fine with it.
There's already a precedent for that. As a suave, conniving arch-villain, I've found that Michelle Gomez makes a much better Master than John Simm. In fact, Gomez reminds me of the classic Masters like Roger Delgado & Anthony Ainley far better than Simm ever did.