He had to be male but they could have gone for non white ... I don't think gender reassignment is part of regeneration)

Artistically speaking, a female doctor would enable - literally!- dramatically different stories but I am pretty confident that such considerations are overridden by the commercial risk such a fundamental change would be.

Completely independently, my daughter and I came to the conclusion that while an Indian, Chinese, ... doctor would be possible the co-incidence of changing to a black doctor at exactly the time the US changes to its first black president would attract all sorts of bizarre criticisms that would not have occurred a year or two ago or in a year or two's time. And as before, the commercial concerns would want to avoid those.