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.

At this point, I honestly have no idea what an-caps think. I presume that most of them don't think.

I actually stopped paying attention years ago, and before that I was only paying attention to argue with them.

They had some valid points early on, and actually including the observation that the unregulated exchange of goods and services is a natural human behavior. They just went wrong pretty much immediately after that observation, when they conflated that unregulated exchange with "capitalism" and expanded it out to the stipulated system to which each and all would be necessarily subject. They could never seem to wrap their heads around the fact that that position necessitated the institutionalization of authority, even though they spent most of their time and effort trying to dream up "anarchist" states with "anarchist" laws that would be enforced by "anarchist" police and an "anarchist" legal system. That and spluttering self-righteously about how it all didn't actually count as a state because blah blah blah.

But in the wake of the Great Overton Window Shift of 2009, when the Republicans co-opted the Tea Party protests and turned them into a traveling carnival of hate, a bunch of conservatives started identifying as libertarians, so a bunch of libertarians started identifying as an-caps, and the intellectual level of an-caps went from amusingly mediocre to frustratingly low.

Presuming that that trend has held (and judging by the rest of right-wing politics, it's likely that it's not only held, but accelerated), yeah - I would presume that most don't even know.

Yup. They do. Not only are corps legal fictions, they're supported by IP law and a whole host of regulations that allow them to grow to such massive sizes. Limited liability is cancer.

and either don't consider at all what happens without a government if people break the (quite arbitrary, but they don't think that) rules of capitalism

Of course it's considered, and there are a handful of possible solutions.

believe whole heartedly that government regulation is the only reason why either guns, private arbitration, or smart contracts haven't already solved that problem.

Trade is a technology. Force freezing human economic interactions into rigid capitalist guidelines prevents actual development. Some people would just like to see problems solved without violence.