Logic problem: The founding principles of the U.S. and Christianity.

[Rokcet Scientist]

Isn't the history of the U.S. from it's independence from England to the present proof that we were supposed to have separation between church and state.

Yes, if you look at it like that within that limited scope you could get that impression. But if you take a step back and include the real 'start' of the country/nation, 1620 – 1776, the cultural foundations of the US, and the current outlook for the next decade and century at the other end of the scale into your perspective then an entirely different picture emerges!

I don't see how things could have developed the way it did if this weren't so.

Because they didn't. They only appeared to develop 'the way they did' from a limited perspective. Standard illusionists' principle.
Broadening that perspective, taking a 'helicopter view', changes everything!

If this country was founded as a Christian country with no separation between church and state, a religion would have taken over by now.

Should magic underpants boy or pro-life boy win the WhiteHouse, they are effectively doing just that! Even Obama kowtows to the churches. Of every religion

In fact, given the numbers of different religions groups that settled here, wouldn't there have been several religious wars by now?

Unprovable speculation that involves so many more factors. But with stuff like Waco, the Tea party, and those hypocrite candidates bending over backwards to be more Xtian than the next guy, the US demonstrate that they are uncomfortably close to that situation.

Besides, what were the 2 Iraq wars, the war in Afghanistan, and the incursions into Somalia? Whatever they were, conveniently, they also were religious wars!