I'm not here to debate the death penalty; that's for anothr thread. Let's stick with whether the US is a governemnt shall we?
I appreciate as an American your government gains its legitimacy from the people, as all democracies/republics do, and all countries should IMHO.
However you confuse legitimacy and authority - there have been many non-democratic governments that still exercise authority without the legitimacy that democracy bestows.
Yes, the continuing membership of the CITIZEN <in> the CONGRESS and other BRANCHES OF GOVERNMENT give the US legitimacy, as membership of other associations (state, federal or otherwise) gives legitimacy to those associations.
However, the US has no inherent authority, no authority which is not delegated to it <by the people>, and that authority can be removed by reversal of that delegation decision, i.e. abrogation of the CONSTITUTION concerned.
Inherent authority aka sovereignty is the defining characteristic of an individual - something the US is not.