I have to say the very false foundations of Catharism would have literally died out on its own.
Such church-state functioning and alliance is alien to the NT church. The only one exercising in such a fashion was Saul of Tarsus and we know the rest of his story.
It also alien to our founding. Oh the founders knew of this history and the current ongoings. That is what makes us different.
-— Such church-state functioning and alliance is alien to the NT church. -—
In Catholic countries the Church was separate from the State, even if the State religion was Catholicism. It sounds like a contradiction, but there is a real distinction.
The Constitution allows states to have established churches, though they no longer do. It’s a subject worth reconsidering, because we need an intellectual basis for suppressing Mohammedanism.