>The US government is abolished, but the legal system is preserved? Not how it works.
I said this was a thought experiment to sort of isolate this one issue. It's how we (praxeologists of law) might give suggestions to the polycentric legal system rising from a previously state-ruled region.
You might not have this misunderstanding but many do. Anarchy simply means a lack of rulers. It doesn't necessarily entail chaos and it certainly doesn't mean a lack of law.
Anarchist libertarianism or anarcho-capitalism is distinguished from early leftist-"anarchism" by two main characteristics.
The former is radically and uncompromisingly for free markets and anti-state, with a focus on sound legal theory (a combination of a set of static legal grundnorms, viz. the praxeological aspect or a set of laws reasonably suited to all humans, with room for free variation among groups/cultures understanding that personal ideology will shape jurisprudence).
The latter—leftist-"anarchists" as you'll probably see protesting the next Gx Summit or depicted on the TV—make varieties of socialist or communistic ideological proposals which results in a total lack of consistent legal theory. As an ideology, "an-cap" is relatively new and our body of attendant legal writings already dwarves theirs. Where leftist-"anarchism" has been tried, it's failed to maintain civil order and the "leaders" have been nigh-indistinguishable from other despots.
>There would be a vacuum and a brutal rush to reappropriate resources according to rules other than property rights, which ceased to exist along with the government.
You'll probably get that anyhow if you are so unlucky to live in a country that implodes and it is more likely that most people will just go on following the status quo than you and others being so swayed by my words and we see an orderly unwinding of your gov't.
Throughout civilized history, from tribalism to today, we've seen paradigm changes. What's next when democracy fails? Ideology and law can both be seen broadly as "technologies". A few of us are working on a backup plan. Most people who are even interested involve themselves in electoral politics and/or try to use the web for "smart gov't".
>What's to stop me from building a militia and taking over a town? Taking your house and wife? I've got overwhelming force and I say they're mine.
The simple answer is that feuding is expensive, even more so of a drain without a mass of people to extract wealth from to fund wars.
Really though, if you were concerned with these objections you'd realize you already live in such conditions and become a libertarian anarchist! You live in a state (geographic monopoly on law, arbitration and the use of violence).
Democracy is an insidious advancement in ideological technology because it gave the populace the idea that "anyone can be king". The US was a noble experiment but I consider it a failure. You have a massive drain on standards of living from bureaucracy and regulations, meanwhile the political elite is not much different than in previous paradigms.
Why take houses by brute force when you have everyone in them convinced that X/Y/Z must be provided by gov't, and that gov't needs it's "revenues"?
Polycentric legal orders similar to what we propose have maintained civil order longer than the US has existed so far[0]. It was just after WW2 that the dollar upended the pound sterling as the world's reserve currency and there was a sudden huge rise in prices and chaos in Britain.
It will be an interesting chapter in history for how long the US maintains its global hegemony. Why not, with half of world military spending or whatever doesn't the US just start picking off little countries here and there like you say? Well they sort of actually do by proxy wars and "economic warfare".
At a basic level, governments are in a state of anarchy amongst themselves though. Why might it not work at other levels? I'm convinced that we can have what's promised by states but under-delivered by abolishing them. A lot of those suffering the sort of Stockholm syndrome concomitant with statism see what I am saying as crazy but I'm unconcerned.
This is one tactic on bringing about libertarian anarchy and many who in debate will say they oppose it actually are helping bring it about[1]. If you want a more in depth answer to your actual questions see here perhaps[2]. A DRO is a startup too ambitiously frightening for today's YC, but it actually funds many who feed into said tactic. Legal praxeology is just a hobby for myself and I doubt I'll live to see my dream of a free society, so I am working on a large global health problem which again is part of the tactic.
[0] https://mises.org/library/medieval-iceland-and-absence-gover...
[1] https://web.archive.org/web/20140530221508/http://www.anti-s...
[2] https://www.youtube.com/watch?v=jTYkdEU_B4o