[dragonwriter]

> The argument for goes back to Hobbes

While it resembles Hobbes description of the Leviathan, and is in some sense a product of it, the definition is more directly product of fairly modern political science seeking to systematically define it's scope of analysis and the things it is addressing in ways that don't apply only to a narrow cultural and historical context than it does to Hobbes’ normative arguments.

> Thus the people have the ultimate right to legitimate violence.

That it makes a genuinely democratic state also one in which the state or government is the people is more a feature than a bug of the definition. (Though whether actual modern Western regimes are genuinely democratic is a question for which analysis of particular states has frequently suggested a negative answer.)