Originally Posted by
Antigenes
Papal temporal control had relatively little to do with papal religious authority in Western Europe. Take the Three Chapters controversy of the sixth century, an appropriate starting point. Basically, in order to force a compromise with the anti-Chalkedonian prelates of Syria and Egypt, Ioustinianos attempted to ban the so-called "Three Chapters", three writings made by supporters of Chalkedonian orthodoxy that, according to the anti-Chalkedonians, were basically Nestorian heresy. Pope Vigilius disagreed (took some balls, since he was the Emperor's "guest" in Constantinople at the time). As per Wood (in Chazelle and Cubitt, 2007), the Papacy had enough muscle to force virtually all of the Gallic bishops to take the Pope's line against the Three Chapters. And this was in the 550s, before Gregorius I, when the Papacy really started making things happen.
The popes already had a significant amount of weight to throw around even before the Western Empire fell. It's fair to say that a lack of centralized authority may have messed with things in Italy, but I doubt it. Caesaropapism as it was in Byzantine territory was intimately connected to the need to mediate among the Pentarchy over the issue of acquiescence to Chalkedon, and later caesaropapism evolved out of Zenonic and Ioustinianic practice in attempting to solve schisms without reference to religious councils and so forth. The Papacy won't really be connected to that controversy without Byzantine control over Italy, even if the Ostrogoths, Lombards, or whomever does establish some kind of stable semi-centralized authority in the peninsula. It wasn't a simple "temporal rulers kept the uppity popes down" situation at all.