In a case two defense agencies are representing clients on different sides of a dispute, they would have to sit down and work things out so both parties get a fair hearing.
But that isn't so. They don't have to sit down and work things out. One or both can choose to use force. You say that they wouldn't because it wouldn't be in their interest to do so. But they may not know that, they may not care, and there will be times when it will be in their interest - in the sense that they can get away with it. As Joe says, your assumption that defense agencies will sit down and work things out is an assumption that can be applied to people - we could say that individuals will sit down and work things out and that would mean we don't need defence agencies.
You point out that government is often the aggressor (initiates force). That's true. In the issue of the initiation of force versus the respect of individual rights there are four possible types of actions: Private party actions to violate rights, private parties actions respecting rights, governments actions respecting rights, and government actions violating rights. This points out that it is the nature of the act, not the actor that should be our focus.
Anarchy is a self-made blindness to the use of government to protect rights, and a blindness to the fact that government can't be thrown out for long since warring factions that will arise in the absence of a government will soon lead to a monopoly on the violation of rights by the strongest group of thugs. A proper government is the only hope.
You really need to read Joe's article again and try to answer his arguments more carefully.
I would still argue that it [the right to take whatever risks they want] is a risk people should be free to take, and that people are better off having even the nominal freedom to secede if they mistrust an agency's policies, than being forced to rely on the good graces of a monopoly state, and having no recourse whatsoever if the government becomes a dictatorship and decides to throw them in a concentration camp. Also, it's likely that insurance policies would exist to provide for emergency protection in case someone's defense agency did become a dictatorship and try to prevent them from leaving, is that became enough of a problem.
Who grants and provides the right to secede from a defense agency? There is no magical Anarchy Fairy that will make defense agencies protect rights if they happen to think they might profit from violating them, nor will that magical fairy protect an individual's right to walk away from a defense agency. With anarchy there is no market free of the use of force, so competition will include the use of force, so anarchy can't bring justice any more often than it brings injustice.
Again, if there is a government based upon individual rights, then we want there to be a monopoly of those rights, and those laws. To say otherwise is to repudiate the very concept of rights. Just as there is but one set of natural rights, there should be but one set of laws. And if they aren't enforced, they aren't useful, and it is rights that aren't protected.
The NAP covers the legislative part of that. The judicial system could take multiple different forms. A system of common judges would be one example. I guess the biggest issue would be deciding who is qualified to be a judge and who isn't, which would require some sort of agreement among the various agencies.
I'm sorry, but that makes no sense. Why would everyone agree to NAP? And how does that happen - do we all answer some kind of call to go to a meeting in our neighborhood and shake hands? And if it isn't an enforceable agreement then it is just a kind of intellectual masturbation. If it is enforceable, it is a call for a centralized authority of some sort. Either it can enforce its rules or it can't in which case it doesn't answer the problem. The ABC Progressive Defence Agency won't accept any judge that isn't in favor of forceful redistribution of wealth. While the Libertarian Defence Agency of New York won't have any part of that. Agreement? No way. And when a judge, any judge, makes a ruling, there is no ability to enforce it but to use force - and there we go, the use force by one faction against another.
Here's a question: Let's say that some sort of organization exists which is analogous to a government. Now let's say that someone decides to start a defense agency which exists outside the government. They only enforce their laws on consenting clients, they do not initiate force against anyone outside the agency...
If the agency has its own laws, and they can enforce them on anyone, then people can find themselves subject to rights violations. Why advocate for a system that encourages the 'legitimazation' of laws that violate rights? What you are advocating here is identical to an organization that arises to enforce Sharia law on all who join up. Voluntary Sharia is far, far better than involuntary, but why would you want it? And how do you enforce the voluntary nature of the membership? You can't without a government that has at least some laws and some powers of enforcement that span the entire geographic area and include the Sharia organization and its members. If you don't have that you will have forced Sharia arising and you will have no way to stop it. If you do have that, you don't have anarchy.
Meanwhile, the judicial system is altered so that judges are appointed based on mutual agreement among all existing rights protection agencies, including the government (Or, to be more practical, an established system which in amenable to all existing agencies), all defense agencies are given the right to petition for a judge to be removed from the bench in response to a particular grievance, and all affected parties are allowed an equal voice in this process.
Who alters it and how is it altered? Is it done by our current legislative/constitutional organization? What is the remaining structure if not a monopoly of law that forces all of the new "judicial system" elements to adhere to the new agreement? What if some of them just go their own way and don't abide by the "mutual agreement" - if there is no enforcement it doesn't work. You say all defence agencies are given a right.... given by who? Enforced by who? This is a fantasy game where floating abstractions - ideas untethered from reality - pop up like endless Whack-A-Mole non-explanations.
Now, keep in mind, any rational person will choose to seek a peaceful process, and the government would have a right to refuse to negotiate with anyone who is not willing to negotiate in good faith.
In the real world we have to deal with terrorists, with people like Hitler, Stalin, Po Pot, as well as with the garden variety armed robbers and thieves. Saying that government would have a right to refuse to negotiate with anyone not willing to negotiate in good faith hardly addresses real world problems. And where does this government get this "right" of refusal? Governments don't have natural rights - only individuals do - so it must be a legal right. What is the structure that includes both the government and those it refuses to negotiate with, and that defines and maintains that legal right? Who decides what good faith is in any particular case?
If you are a rational person, you will sit down and think about these issues and realize that even if you don't agree with the logic that anarchy could never work, that you will see that it would be immeasurably easier and more likely that a government could be built and maintained that did a far superior job of protecting individual rights than any of the convoluted anarchy schemes - and protecting individual rights is the purpose behind the entire discussion.