While states dominate history, private law has proven successful. You could see the Law Merchant throughout Europe as one example or medieval Iceland, where civil order was maintained for longer than the US has existed so far, as another.
> You could see the Law Merchant throughout Europe as one example
That is not an example of justice in the absence of the state. All the principal trading cities were governed, whether as city states (Venice), as quasi-independent city states within a federated league (Lubeck, Hamburg, and the other Hanseatic States) or as cities within national kingdoms (London, Ipswich and other cities under the English crown). It is an example of states agreeing to standardized laws to attract traders and provide a solid basis for ongoing trade.
From the Merchant of Venice:
The duke cannot deny the course of law.
For the commodity that strangers have
With us in Venice, if it be denied,
Will much impeach the justice of his state.
Since that the trade and profit of the city
Consisteth of all nations.
The presence of common merchant law does not mean the absense of a state.
I said private law, not purely anarchic examples. I could give more anarchic ones if you liked but it's revisionist history so you'd have to do a good bit of reading to really discuss it.
Iceland is an example of polycentric law fairly close to what anarcho-capitalists advocate. You didn't really address that or the other points.
The first big difference between the Lex Mercatoria and present-day law is the source being jurisprudence and not bureaucratic legislation. The second would be cases being torts with an identifiable victim versus today's with victimless "crimes against society".
For why legislation is awful and for a hint at solutions under an eminently human system of law in a free society see these:
That is not an example of justice in the absence of the state. All the principal trading cities were governed, whether as city states (Venice), as quasi-independent city states within a federated league (Lubeck, Hamburg, and the other Hanseatic States) or as cities within national kingdoms (London, Ipswich and other cities under the English crown). It is an example of states agreeing to standardized laws to attract traders and provide a solid basis for ongoing trade.
From the Merchant of Venice:
The duke cannot deny the course of law.
For the commodity that strangers have
With us in Venice, if it be denied,
Will much impeach the justice of his state.
Since that the trade and profit of the city
Consisteth of all nations.
The presence of common merchant law does not mean the absense of a state.