Yeah, TBH, I simply don't get the logic behind the initial premise here. Did the Pope declare the HRE the only empire in Europe, or what?
In 800, there was a basis for equating the HRE with a re-unified Europe. France, most of Italy, and most of modern Germany had all been unified under Charlemagne. Only Britain and Spain remained outside the HRE. In future years the HRE contracted, but there may have been an old dream of a unified Europe in a single Roman Empire. Maybe someone can confirm or deny this last part.