This must be why Catholic Switzerland was a republic long before the reformation, eh? And why the barons of a Catholic England wrote the Magna Carta?
The idea that church government should be selected based on what sort of civil polity we want is worse than backwards; it is absurd. Jesus and the Apostles established a church government: you can see it clearly in the Pastoral Epistles and in the writings of the early Fathers. It's not ours to amend, throw away, or modify.
Oh, BTW: heaven is a monarchy, not a "republic" or a "democracy". Was yesterday, is today, will be tomorrow. Get used to it!
Almost certainly drafted by the Archbishop of Canterbury, Stephen Langton, btw.