You don't glass everybody immediately. Nuclearia basically does a protection racket. Do what we want, or we progressively make an example of you. Each "round" is 1) issue demand 2) if no compliance, respond with N units of force 3) N++ 4) repeat until results. Rebels get the Alderaan treatment. Rule by fear. Either every country decides to let themselves get scorched to prevent Nuclearia taking resources as a last FU, bend the knee, or re-arm. But one well-placed rebel ICBM ought to dissuade Nuclearia from their racket.
Having some subpopulation (police or even military) with guns but not the populace is a similar power dynamic. It doesn't take many "rebels" to make the hegemony think twice about a takeover. But a complete monopoly on power means a "clean sweep" military coup with minimal bloodshed is possible. My finding of the world is that most people just want to live their life and do their thing. So in such a takeover, I believe most people would just fold. But a small rebel % can turn that bloodless takeover into an indefinite boondoggle.