Had Edward the Confessor made William his more obvious successor and had the witan supported William (with harold doing so as well) how would everything have been different without armed conquest? Would England and the world be different today?
The real question is... how do you get Harold to support his claim? Harold is NOT going to support William's claim. Not as long as he's alive, and he had the pull with the Witan and the king to get his way, as was demonstrated when HE was named king over the king's legitimate heir.