I just saw this post and wanted to point out my problem with this mentality - it's absolutely fine to think the Doctor should be a male - he has been for over fifty years now, and I can see why changing something like that might be problematic for long time fans simply because of the mechanics of the ongoing story and such.
However, I hate, hate, HATE the idea that white males NEED other white males as heroes and role models. That's absurd. I'm a non-white male - does that mean the Doctor couldn't ever be a role model for me since I'm not white? Of course not. I love the Doctor because I feel a connection with the character - his empathy and humanity and intelligence - not because of what he looks like.
Those core values are things that won't change whether he's white, black, male or female. This idea that white males need white male role models is part of what perpetuates race/gender issues. I'm certainly not advocating that every piece of popular culture needs people of colour, females, LGBT characters, etc. as their main characters, but I do think that people who feel like the increasing trend towards incorporating more diversity is an attack on the things they love need to take a really hard look at themselves and ask themselves why this is the case. If the Doctor were to become female, does that mean Doctor Who is no longer an appropriate role model for males? Even if the core values that have been around for over half a century remain the same? I don't really see it that way.
You have made the point most excellently; far better than me. Somebody somewhere, in a fit of political correctness, might think changing the Doctor's gender and or skin colour will somehow make him more inclusive? Encompassing? Universal? Appealing?
He's a madman with a box, two hearts and a sonic screwdriver ffs. The Doctor is interpreted through his companions. Let THEM be diverse.
That said, I still believe that white males, and young white males, DO need good white role models, and I believe the Doctor is one of them and should be left well alone. Yes, they need good FEMALE role models, and good ETHNIC role models. But I think it's a good thing for boys to see such a positive role model that stands against an impression that being a white guy is only two steps away from being a Nigel Farrage or a Biffer.
That doesn't mean The Doctor doesn't have universal appeal - of course not. I'm not saying we need to use the Doctor's gender and ethnicity as a stick to beat minorities with. But if admitting that I prefer my Doctor to be a white male makes me a racist misogynist then fine, I plead guilty.