> Imagine a society without justice/police in which people must fend for themselves. It would quickly deteriorate to the point wherein there would be a fair bit of violence.
that conclusion is not warranted by the premise. How about this as an alternative outcome: "Imagine a society in which people actively defend community values for themselves and in cooperation with a community of similarly concerned citizens. It would quickly stabilize into a mostly non-violent community."
What are police, but a group of people specifically dedicated by the community to a specific task? Just because there is no dedicated, professional person filling a role, does not mean the role will not be filled.