But then I think the ones that did change, like the one mentioned in The Doctors Wife, were gender fluid or non binary.

Excellent point! Time Lords certainly seem capable of changing gender if they wish too, but it would be odd to me for it to only come up now with the Doctor when he's regenerated as male so many times that it would suggest that he *does* consider himself to be a man? Ditto with River, I can't really picture her as deciding to regenerate into anything but female. Again if the right casting came along then maybe I wouldn't be opposed to it, but it's not something that I'm picturing right now for the character as established