While I agree with your sentiment, the problem with the Bible is that it doesn't contain democracy. It only really has examples of god ordained despots. So one can "follow the Bible" and have results that are wack.
Israel was supposed to still be loyal to King David even though he was a liar, murderer and adulterer. Jesus has the opportunity to tell people to reject Caesar but instead choose to more or less tell them to let Caesar be Caesar and keep whatever is God's separate. It was tacit acknowledgment that sometimes you have to obey evil rulers. (St Paul carries this on in Romans)
So obviously that was necessary in first century Judea. The problem is that's the only scenario the new testament deals with.
Add to that that all Jesus' ethics are person based, without a single word of what a government should or shouldn't do. Minus all the common sense tradition amalgamated in Europe over 1600 years, and you have the religious right of America.