there is a problem, but it's cultural rather than racial.
Bingo. Nothing about being black means you must commit crime. The thug culture is the problem. And to get back to the original topic, a list of places to avoid would be just as useful to a black person who didn't want to be raped, robbed, and murdered as it would to a white.
Why do you believe that a female Doctor Who would not attract and keep TV viewers?
Indeed. Why not cover all the PC bases, as the OP stated? "Why not a vegan tranny black lesbian Muslim in a wheelchair?" For me, the Doctor will always be Tom Baker. But then I'm a straight white male. May my oppressive soul burn forever in Hell.
If all else fails, lower your standards.