I guess I hit a nerve, aye? Sorry Octavia. Good questions!
God established Israel as a theocracy to rule the world, with Him as head, until they rejected His rule and asked for a King like other nations. "they have rejected me from being king over them" (I Sam. 8:4-18) He appointed a "King" Saul, along side the High Priest, and so began the separation of "church" and state. Later, Babylon and King Nebucadnezzer was endorsed as the first Gentile sovereign govt. separate from Israel. (book of Daniel). Continuing to today. (Romans 13 gives a good summary)
Someday soon, Christ will return and rule the earth from Jerusalem, restoring the theocracy and sovereign rule of Israel over the world. With today's flawed and often corrupt leaders, separation is a good thing, until the "good" King returns to do the job himself.
I agree many early colonies first followed the tradition of the church of England, ruling in a theocratic and tyrannical way, but eventually they all agreed that separation of powers was the best way. Church and State EQUAL but separate.