"Suppose Joe Blow managed to raise a private army and overthrow the US government, then impose a vicious totalitarian regime, hated by everyone."

You are missing basic information about what America is. Imagine a country which has over 200 million kings/queens. America has been an republic for over 200 years. A republic is a country which recognizes that the sovereignty resides within it's citizens. Also United States is just that, a federation of states bound together by a constitution- the federal govt's power resides in the constitution- no constitution; no federal govt. No Federal govt, leaves you with the power of the individual States- which also have their own constitutions.
The US miltary serves the people of United States, it under the command of the elected President of the US with a succession as stated in the constitution if President is disabled [killed, captured, or too ill to command].
In other words you can't "raise an army and overthrow the US govt", the US citizens simply do not recognize that this power can captured by miltary force- if leadership is captured or killed, we simply elect new leadership. Capture Washington DC, and we move the capital somewhere else. There is nothing unique about the people who represent us- other than we elect them to represent us, and to remain our representives they are required to follow the Constitution.

Btw, the Framers saw that a republic is the natural/actual state of things. In other words Americans should see that the ultimate sovereign power of any country resides in it's people and that any recognized sovereignty [be it benign king or foaming totalitarian dictator] is granted by the consent of it's citizens. Also international law "sees" sovereignty as granted by consent of it's citizens.