Let me put it this way. How do you think property emerged? Was that a purely 'voluntary transaction.' Of course not. The vast majority of 'property' that exists now has been essentially taken from someone else violently. And if it wasn't then that's probably because whoever claimed it for themselves had enough guns, mercenaries, 'money' or sheer influence to make contesting it pointless. The fact that something like the United States as we know it even exists should tell you something about the 'non aggression principle' and how viable it generally is IRL.
In Western societies, we have this principle called "presumption of innocence". Thus, unless someone can prove that a particular piece of property was stolen from them or their direct ancestors, the current owner of the property is presumed to have acquired it legitimately. Lockean homesteading theory teaches that previously unowned property can come into private ownership by the mixing of a person's labor with the unowned property.
So? Again,
none of that would exist in the first place if we had followed the non aggression principle. Plus the legal system you cite is by definition based upon coercion for enforcement (taxes, prison, etc.). Besides even if we were to abolish all that over night and implement the 'private court system' you dream about
somehow, it would still boil down to two things:
1. Who was better armed.
2. If people had some sort of strong incentive to play along with the people claiming to make the 'rules' (threat of ostracizing, banishment, etc.).