That’s what Peter Heather makes readers ask in The Restoration of Rome:
Thanks to Charlemagne’s attentions, the papacy was enriched, visited, courted and paid enormous respect, but all these gains came with a price tag. The emperor’s respect for the papacy was genuine, but he was equally convinced. . . that he had his own hotline to the Almighty. No mere vassal of St. Peter, he had no hesitation in making use of the papacy for his own purposes . . . for this too was God’s will. Nor was Charlemagne afraid actually to disagree with the Pope — even on matters of doctrine. The example par excellence is the Council of Frankfurt. There and to the Pope’s face (at least, to those of his legates) Charlemagne had his churchmen declare that Pope Hadrian’s acceptance of Constantinople’s new teaching on icons was in fact mistaken. A second, less charged example is provided by the famous filioque clause. . . .
As such, we can place [Charlemagne] firmly in a tradition which stretched back for the best part of half a millennium. From the time of Constantine onwards, overarching responsibility even for the identification of correct doctrine had been part of the Christian ruler’s job description, and Charlemagne’s attitude to Rome was nothing more than its direct continuation. Indeed, it would be extremely easy at this point to go through the same checklist we have used before, and come to the inescapable conclusion that Charlemagne was undoubtedly the head of the Church within his domains. He appointed all the leading churchmen, he called all the major councils and authorized most of the rest, and great tranches of legal directions on the practicalities of both clerical and lay piety were drawn up in his name. (332-33)
So much for that audacious papacy. Turns out the Pope would not have been the official he turned out to be without the audacity of the emperor. In fact, transformers of culture, Roman Catholic or Protestant, will never see their hopes for a Christian society realized until the ruler embraces the faith and enforces it. Not even Boniface VIII in all his pomp and show could make Europe Christian. It took emperors, kings, princes, and magistrates.