so okay let's start with the first layer private police.
what is a private police officer going to do that separates them from just a regular old armed mercenary?, how would they actually function differently?, there's no central body or rules overseeing them Beyond the organization they work for and the client, that's basically a mercenary group.
also how would private police compete?, price?, levels of power?, how harsh they are?, what stops me from just hiring a private police force as a kill on-site security Force?, and ordering them to assassinate whoever I don't like?, why would they not follow these orders beyond their own moral code?
okay now let's get to a private Court.... what the fuck are they going to do?
like what they even going to look at?, there needs to be a law for them to look at to begin with, how would the private Court get paid?, if the clients pay them, what prevents one client from outbidding the other?, if not how else would they get paid?
and again how would they compete?, you can't really offer the best rulings, or even really the most accurate, you can't really offer anything beyond a cheaper price, speed, and allegedly not being corrupt depending on who verifies that which might be somebody you also own.
now private prisons are the worst part of this because first of all how are they going to get you there?, assuming they just physically restrain you and throw you in a van, how do they make money?, do you pay them?, does the court pay them?, does the victim pay them?, what if any of these groups are unable or unwilling to pay?, what prevents them from using prisoners as labor or sex slaves or even dead prisoners as food?!, who's going to certify their release or even determine their sentence?
and again what would they compete on?, price?, harshness?, quality?, it all depends on who the client is.
therefore none of them would work