I think you are confused. First off, regarding government. God is indeed Lord of the universe, and He provided humans with His law, the Bible and He told us, that is all we need to govern ourselves. All we need is a justice system to apply the laws. And an enforcement system to apply justice.
When the people of Israel asked for a King, God attempts to discourage them, saying it is a bad idea. They had a justice system in the form of "judges". As there were multiple judges, there was some checks and balances should a single judge become corrupt.
In times of war, leaders rose up to lead the people, but even they were subject to God's law. God clearly understands His creation. Ever since Eden is inclined to sin and sin leads to corruption.
Power magnifies that corrupt nature of man bringing out his or her worst qualities.
The people wanted a King to organize them to extend their power over others and to create a secular empire like those around them.
Read the books of the Bible related to the kings of Isrrael. Understand these books "mock" the kings by showing how each was corrupted by their power. Understanding the underlying message of that corruption, we understand why God discouraged the concept of "kings".
Jesus is not about power, but rather the forgiveness of sins. He is clear, He came not to judge man, but to save man from his corrupt nature. The morality Jesus preaches is a clarification of the original Jewish law and as such even Jesus feels bound by God's law. Most powerfully, the Bible makes a point, that the Devil offered Jesus the whole world if He would bow down to the Devil. Jesus rejects the offer. This is perhaps Jesus's strongest statement regarding his purpose.
Regarding America, unlike most nations at the time, the US was founded on the original principle that God was the Creator and endowed all humans with unalienable rights as sons and daughters of God. We rejected the corruption of Kings, and instead everyone including Presidents became subject to the law as was the case in early Israel.
Then starting with the Constitution, we began to enact secular laws to govern society just as the Bible has religious laws. In that sense, we were the "new" Israel... a nation under God guided by what our founders determined to be God's laws.
It is true we have become to move away from those principles and the consequences have not been pretty. After two centuries of trying to realize the aspirations of equal rights for all, our society has suddenly embraced Marxism, where human rights do not exist.
