IMO you have the cause and effect here completely backwards.
Zip ahead to US colonization. Why did people come to North America? In many, if not most cases it was to escape religious prosecution or the blowback relating to that persecution.
There's a limit to how large your kingdom can be if people are repeating your orders and those of your court from memory.
That's a common western viewpoint. I wonder how the 'warring barbarian bands' felt about the 'cultural standardization'.
Check out the story of Alfred the Great in England. The story of England and the UK is the story of Christianity's development. The Saxon, Welsh and Norse pagans were certainly and rightfully not happy with how that transitioned, but ultimately the outcome was almost certainly for the better.
Not at all, Christianity has always been practiced as a social and political construct as well as a spiritual one. That's the core of it's power. Earthly institutions don't persist for thousands of years otherwise.
You really need to look at more ancient practices that are further away from modern practice and politics. Places like England and France were transformed from a collection of warring barbarian bands to nations by the cultural standardization brought by christianity. Later reforms were driven by schisms like the reformation and other things.