> The definition of the state as the "monopoly on violence" only works if you think that states inherently have the right to their power.

Not at all. The idea is that the state has a mandate from its citizens to exercise violence (within due limits) to enforce the decisions of the citizens. It's a monopoly because citizens don't have the right to use violence against each other, and even if they do the state is guaranteed to be able to respond with enough force to make it stop.

> In effect, Americans have contractually given the state the essential powers of violence but still keep the means to take that power back.

This justification to arms ownership always strikes me as delusional. Whatever the amount of weapons in circulation there is absolutely no way American citizens could fight their own police and their own army.