And yet, you show a naive or short sighted side your self. Arguably God did in fact want the church and the government to be one and the same. He set it up so that the priests did basically run the government. He always wanted to be the king over Israel but the people decided they needed a man thing that they could see. He stipulated that His people choose kings and leaders who knew the law. Which is to say the Bible. One of the chief duties of the king was to defend the faith. It has always been man, in my opinion, that wanted to separate God from government. And while I am not advocating for a theocracy, as we have it separated God even more from our government, how is that working out for us today?
You need to read your Bible again. They had kings in the OT, but the NT government was set up differently. Just think of the Muslim countries and Sharia Law - that isn’t what we want as far as having religion at the helm of our government, now do we?