Why would anyone find this convoluted social order desirable in any way?

Because it implies a bunch of value added labor - investigations, peaceful civil arbitrations, equitable adjudications, amicable and fruitful conflict resolutions - that don't exist in the real world but seemingly should if liberal theories of social order are accepted.

It's a fairytale of civil justice, told by babies to babies, to soothe their own anxieties about the civil nature of the modern world.

Any time I'm a victim of a petty crime I have to get an arbitrator to prevent corporate warfare over my insurance payout?

You make a single phone call and everything sorts itself out.

Absolutely Utopian.