I think we should keep in mind when and where the show was originally made. The show was produced for the BBC in the early 1960's. In the context of 1963, would they have contemplated making The Dr. female? If they did I doubt she would have been considered the lead of the series. Indeed, from what I know, The Dr. wasn't supposed to be the lead. I think this would mean making the other Timelord character "The Dr.'s grandson"-and I think it would be tempting to transition the show towards making him the lead or at have him the Dr.-especially when the woman playing The Dr. moves towards retirement.
If the show premiered now, this wouldn't be an issue. But this is 1963 we are talking about-it was a different time culturally speaking even when compared with a few years later.
In an older thread about what would have happened had no one thought of regeneration, one method for dealing with Hartnell's retirement was basically to promote Susan-the Dr.'s granddaughter-to the role that the Dr. had served until that time. This could involve early changes to the series. Susan was reportedly originally conceived as a much more active character than she ended up being. The fact that the character didn't end up that way may be evidence against the idea of The Dr. being female in that context. If Susan had been written as a more active character, and stayed on the series longer, there might have been a small possibility that character would be allowed to take over the Dr. role when Hartnell leaves. This would probably mean promoting the companions to a more prominent role in the series than they had had to that point. It could mean changing the name of the series unless some narrative reason for her taking over the Dr. title could be found. Of course, the actress playing the part is eventually going to want to leave, and having her take over means that no one has thought of regeneration, which makes replacing her a bit complicated. I suppose someone could think up the idea when she leaves, and have some handy explanation for why the original Dr. didn't regenerate.
However, once Susan becomes "The Dr." the role could remain female.
Having The Dr. regenerate into a female form could be an easier way of pulling this off, not sure when that could have happened.