Yes, private law will be just like statism. Probably worse in many respects. But the OP is the wrong way to approach this topic. The proper approach is: private firms will still use violence based on the worst terms that society can be pushed to accept at any given time. The main difference is the violence will be used to defend moral system X instead of moral system Y. And to the extent they use courts, perfectly arbitrary judgments will be made which is no improvement over the arbitrary court systems we already have.