But the roman army and bureucracy weren't gone, it still existed in the Byzantine Empire.
The western bits of the Roman empire collapsed. That's a fact.
Byzantine Empire was the remnant of the Roman empire. That's a fact.
The state church became the Orthodox church and claiming that the Catholic church somehow inherited the right to name the next Roman leader is about as silly as saying that Hindus get to choose the next kind of England because that's the main religion of India which used to be part of the British Empire.