There are smart people out there – people in many ways a lot like me, i.e. borderline idiot savants – who are attracted to the idea that the world needs to be saved through some kind of easy, adversarial revolution; rather than through a huge amount of incremental and cooperative effort. I suspect this is because cooperation seems boring; imposing one's will on others with violence seems fun; and plain old effort is hard and boring. Frequently, these are white middle-class Americans who do not recognize just how damn good they're having it, and how much worse things are in many other parts of the world.
Not in all parts for all things, of course. There are specific things that are genuinely better in other places. But overall, things are pretty great in the US for the middle and upper class. And yet, some of these same people can't stop going on about how awful everything is; and how everything could be much better if we just overthrew the entire system, and replaced it with something completely different. Like, for example: Let us fix real problems in our justice system by replacing it with private courts!
This is all based on the libertarian delusion, the foundation of which is to pretend that some obvious facts of life do not exist; and then coming up with solutions that might work in a fictional world that conforms to those assumptions. In this way, libertarianism and communism are the same mistake expressed in different ways. Both are ideologies that make bullheaded assumptions – about man, about the world – and then try to shoehorn people into it.
The fact of life that people are ignoring here is that not everyone has equal power. If we are to measure power and influence, some people have not just thousands, but millions of times more than others.
Private courts are essentially arbitrage. Arbitrage can work for equally powerful parties. But that's the only situation where it works.
What happens in arbitrage is, if the bigger party has equal choice in what arbitrators they're willing to deal with, arbitrage overwhelmingly favors the bigger party, because the bigger party controls a much bigger chunk of who gets all the arbitrage business than the smaller parties.
Allowing large businesses to dictate terms of dispute resolution effectively prevents class action lawsuits, which are an important way to hold large businesses accountable over systemic abuse.
As the small party in arbitrage, you have no choice. You either go with the corrupt arbitrators chosen by large corporations, where decisions always favor the large businesses; or you don't get service. If there are any payouts, they are such that it doesn't hurt the corporation, and they can continue systemic abuse as a business model, because paying out small amounts from time to time is cheaper.
You either get to agree to use their courts, or you don't get service. Good luck.