Inbreeding has been a problem for the Arabs, just as it was for the Yorkists and Lancastrians ;-).
I know it sounds counter-intuitive but I think the limited gene pool during the War of the Roses produced some extremely bright people. Richard, himself, was a Latin scholar, bookish, highly knowledgable about music, an able administrator and a military powerhouse. His brother, King Edward IV was no dope either. Henry VI might have been a little slow, though...