Agreed, see Weber's focus on government legitimacy. In particular, government's role is to hold a monopoly on the use of force.

I'm not being naive at all, I question the very premises that you take for granted. I don't believe that any group can legitimately claim a monopoly on force, especially when consent is not granted. The justification of a Rousseauian social contract is an example of sloppy thinking, that has been used by the opportunistic to seize power.

It's irrelevant. Monopoly of force is claimed through the threat and/or use of force itself.