Political Memes

Except that governments don't have a monopoly on violence - far from it. Governments have a monopoly on (nominally) legitimate violence.

And in fact, that's an awful lot of why governments establish and maintain laws - to reinforce the distinction between the (nominally) illegitimate violence of "criminals" and their own (nominally ) legitimate violence.

Without a government, that contrived distinction vanishes - all violence becomes more or less equally (il)legitimate.

Now it is the case that the current concentrations of resources that corporations hold would give them an advantage in a power vacuum, but their need to maintain their advantage would sharply limit the amount they'd be willing to invest in governing people, and thus their ability to do so successfully, particularly since they'd almost certainly not possess the presumption of legitimacy that governments generally possess, so would have ongoing expeditures just to maintain their hold, before they could even do anything with it.

I think it's most likely that they'd lay claim to specific parcels of land that would be fenced and gated and patrolled, and in addition to their own facilities, would likely include some version of a traditional "company town," and they'd mostly ignore, other than to deal with and prey upon, everyone outside of their compounds.