This is literally the definition of government used in e.g. social science: https://en.m.wikipedia.org/wiki/Monopoly_on_violence

> private citizens have the right to use force under various circumstances.

Yup, as defined by the government. You can defend yourself in certain circumstances, but you are always subservient to the military and police. They are the ultimate power in the state. If there was a force stronger than the military or police, that power would then be the state.