The Empire would be having a much easier time if they could watch their two greatest leaders cooperate. They would have smoother church sessions, because the pope would make sure that bishops were hand-picked. Also, the peasants and nobles would be receiving their fair share of land, and protection. I would much rather prefer that the king handle land, money, food, and warfare. I would also hope that the pope would be satisfied with only the religious matters. Cooperation is key in a feudal society like this, and it should be maintained.