The Catholic church mandated the rule of Papal power sharing with the King.
The King exercised 'divine authority' - under the 'godly' auspices of the Pope.
They split the profits/taxes/fines, & generally kept the people obedient/suppressed.
King Henry VIII of England resented the Pope's cut & went Protestant, setting up his own church.
AFAIR, the Aztecs were impressed by the brutish similarities of aspects between the Spanish & themselves in this kind of gov't organisation.
It is IMO, laughable to contend that the 'enlightenment' thinkers who helped frame the US Constitution
were positively influenced in this by the perceived depravity of 'heathen' native tribes..
Although those founding fathers also specifically rejected the notion of an 'establishment' church with a direct role in state affairs.
I suggest a viewing of the movie 'Black Robe' for an example of the culture clash in North America.