I'm getting too tired to wrap my head around this tonight, but my first reaction is that this is way to complicated to work in practice. Why is everyone just magically insured? Like how do we go from here to there? How do I know what level of insurance I need to go where, if each individual property owner can require that of me independently? How do they know what level of insurance I have, and how can they detect fraud? Isn't the arbitration just a court system? So then how to fund that without preventing thugs from free riding knowing that if it is underfunded they can steal stuff again? A dollar spent on private enforcement protecting my property would be a better use of my funds than funding arbitrators. So reverse tragedy of the commons again, until it all falls apart when you can't protect your basic stuff.
Discussion
Read "A Spontaneous Order" (Rachels) and "Chaos Theory" (Murphy) for answers to those very good questions.
Obviously, the "answers" are going to bake-in some optimism about the approach, but particularly Spontaneous Order does a very good job of starting from a completely blank slate and building up from there.