Correct me if I'm wrong, but wouldn't the Emperors be able to dominate Papal elections and essentially turn the Pope into a puppet through forcing through Popes friendly to the Emperor and deposing them if they turn against the Emperor.
In theory perhaps. But it would only be a matter of time before a Pope in the image of Innocent III, Alexander VI or Boniface VIII is elected. A pope of this mold is not to be trifled with. Within short time, such a Papacy can gather the support of Latium, the Papal States, varied Italian States, Venice, internal German states, France, etc.. As we see, this happened at numerous occasions, as Machiavelli notes, the Papacy prior to Alexander VI was in a weak position, yet within a short time, the Papacy had pushed out both the Roman noble power factions, pressed the Venetians, rebuffed the French, used the Empire as its hammer, deposed Savonarola, etc...
An Emperor that breaches the Papacy, is likely to face a fearsome opponent indeed. As the Hohenstaufen would learn, the Papacy was not something that could simply be toyed with. Once more, I suggest that the empire submit itself to the Papacy on most matters and make gains that do not incur interdiction. It would be more lucrative to have a powerful papacy on your side to align with than it would be to have a puppet with whom the other lords of Europe soon reject.