He wouldn't be "one of their's" though, he was the last of the Plantagenet kings, the current crop's claims to direct descent from a Yorkist king would be dubious in the extreme.

Personally, I think he should be buried at Middleham, or maybe York Minster. The people of Yorkshire still view him as a terrific administrator of the north, while brother Edward IV was getting fat down south. Most people would like to be buried in a place they had fond regard for, I doubt Richard would have any fond regard for Leicester(shire), he just happened to get killed in a battle there. He has no other links with that part of the country as far as I know. Let him return to Yorkshire, that's my view.