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Seperation of church and state originated from the fact that people FLED Europe to escape church persecution.
I'll give you a different story line: people begun to perceive the Church's influence as a form of persecution. During, say, the Middle Ages, the Church's influence was deemed justified, legitimate -- and it's not out of blindness, stupidity or ignorance -- and, so, its authority was not peculiarly rivaled (if not to replace it with another form of the same thing). This sort of society, even if it might seem strange to you, "made sense." The Church's authority was the more general counterpart of people's identities as followers of the Christian dogma: one did not go without the other.
What is new with modernity is that the institution which makes the link between society at large and individuals no longer is the Church, it's the State and the fundamental change here is the shift in legitimacy: the modern revolution occurs when people replace traditional authorities by that of a State. In the Anglo-Saxon world, it took the form of democracy. Authority was then legitimated by the notion of national or popular consent (the consent of the governed, to paraphrase John Locke). Want an example of that shift? Here's an American variant of it.
During the Middle Ages, a King was King of a certain land strip. For instance, the King of England governed England -- he's attached to the land, not the population. During modernity, as explained above, the government belongs to the people and, so, moderns would say that King Georges III was viewed as the King of the English people -- including colonials. People would fight a monarch's authority during the Middle Ages (think of the Magna Carta which greatly limited the power of English Kings), but the opposition tries to replace a traditional ruler with another. The new thing during the War of Independence is that the LEGITIMACY of monarchy is challenged -- they want to institute a new system where the government belongs to the people, literally.
Once you understand this, you can see certain things in a different light. This separation DID not originate from the fact that people fled Europe and Churches -- it has to do with how and why people no longer perceived their relationship to political authority the same way. Long before this, Shakespeare wrote a play about a man and a woman who CHOOSE their mate against the will of their respective families and Martin Luther claimed that every man was a priest and that each person should be seen fit for the interpretation of religious texts... people became individualists long before they begun to change their minds about the role of the Church.
Besides, if you want even more historical perspectives, the first modern revolution occurred in England in 1688-1689, a full CENTURY before Americans gave it a go. The American colonials who rebelled against the King were full-pledged, state-of-the-art modern citizens. In 1771, they spent well over a hundred years in a very liberal culture, heavily "contaminated" that they were by the ideals of John Locke. Many of them grew in England where Democracy was a FACT. How do you think they react when Georges "abuses" of his power? They do what they just KNOW will work: they foment a revolution to institute democracy.
Basically, I disagree with your analysis of the origins of this separation. For those interested, the framework I used comes from the works of Michel Freitag and Daniel Dagenais -- two sociologists who amply used the notions of symbols, legitimacy and authority in their respective works.