it’s probably just a coincidence you, but rome was seat of political power in medieval western europe after the split of the roman empire.
Look, Rome is ancient, and the Church is ancient. She also is absolutist, but not a monarchy, an absolutist elective republic, the only one of it’s kind.
So let’s get it straight here. She’s neither a monarchy (which is hereditary), nor is she medieval.
Nor was she the seat of power in Medieval western Europe. That would be Aachen.