The Inquisition still reflected a dysfunctional situation. Because someone was wrong with the church, shouldn’t have meant they were automatically wrong with the country. There should not have been anything for the church to need to fix here.
Today we have the opposite problem, states that are absolutely allergic to churches instead of asking them to take government affairs under their wing.
Well, yes. That was the problem with secular authorities being subservient to the church under the era of "Christendom". Secular authorities being in charge without power flowing from the people is worse (communism). That's why we were so lucky to have founding fathers influenced by enlightenment. It corresponds to the free will given to us by our Creator.
I'd remind you that it was not until the ratification of the US Constitution in 1789 that Church and State became two separate entities anywhere in the world.