I think it'd be interesting to have a black Doctor, though.
Why? If it's "oh, what if racism?" then it's not going to happen. They're not going to have him going back to civil war America and have people try to lynch him. It's Family Viewing and this is the bloody BBC. Did you ever see Robin Hood? It was one of the many family shows they created in the wake of Doctor Who 2.0's success. Medieval drama, loaded to the brim with black people who would not have remotely been there. Nobody commented on them, nobody acknowledged them as being different, they were just there.
All Robin Hood-related stuff is just trailing in the wake of Maid Marian and Her Merry Men and Robin Hood: Prince of Thieves anyway!