I have thought about this for many years.
There is fear in your words and no wonder when post apolcalyptic anarchism is portrayed in such a devestating manner that it seeds fear in all to the extent that the very thought of no rulers would mean utter chaos.
If it were the case, then how did we ever get to any point in history from the caves or trees from whence we originated without all being slaughtered. On multiple continents too!
I would in the worst case scenario offer meagre support for a minarchy but only in the absence on anything presently better.
I would much prefer a natural system where authoritarianism does not exist!