Would be cool to have an open protocol where anyone can make an app to hook people up P2P.

> who handles crimes like assault or theft between the various parties?

If it's P2P, then the same as any other P2P transaction. If I pay a random dude to deliver my lunch, and he assaults me, this is handled by the local police. It's a risk I'm willing to take if I choose to trust him. A distributed trust system w/ reviews will help make things safer.

I feel like sometimes we seek 100% safety in a world where that's not possible, and when it DOES happen we point fingers. With a middleman like Uber we can point fingers more easily, but ultimately we're responsible for ourselves.

> who sets up payments and issues refunds?

There are public escrow services such as escrow.com that could be integrated. And there's always cryptocurrency.