My problem with the court system is threefold:

1. It structurally favors the sophisticated party to a degree that I don't feel is (inherently) present in private arbitration.
2. Its edicts are backed by the overwhelming capability for violence of the state. As a rule, I avoid interactions with the state as much as possible for this reason.
3. It completely eliminates the ability of the parties to choose an arbitrator that both find acceptable. The state picks one for you.

I don't think the advantages it provides are worth all that much in civil cases, but I'm very open to other opinions on the topic.