When you say "demonstrably false" I expect a demonstration to follow.
The government exists to serve the ruling class and protect private property. You can call it a slogan all day but I don't mind being quoted.
Riot cops don't get called on corporations. They get called on protesters.
i already went down that rabbit hole and you pretended it never happened.
regulation of hunting, fishing, timbering, mining etc SOLELY to protect "The Commons"
construction and maintenance of parks roads schools libraries, etc, AS Commons
stewardship of state and national parks, forests, open spaces, natural wonders, monuments, etc AS Commons.
etc etc etc.
when riot cops get called on "protestors" (read anarcho-vandals trying to destroy somebody else's shit) this is one of the FEW examples of The State protecting shit that is NOT "the Commons".
but thats your whole argument, and thus it is why your attempt to force that meme FAILS.
NO society can exist without The State to protect The Commons, as well as the rights and property of the individual, though the individual can often protect those rights and property himself, which really works better than The State's measures.