Your assumptions appear to be:
-The Papacy changed in it's power (obviously)
-the relationship between the bishops and state powers was different between the east and west, resulting in higher church authority instead of an eastern model
-eastern influence was completely undesirable
I think the second point is the biggest stretch. The west had it's own share of state influence in the church, as like the east, which can be seen in the local state heads having say in the new Pope (similar to the east's new patriarch selection) as well as the Anglican split (brought by a political struggle between the Pope, English and French [divorce is simplistic and innacuarate])