The collapse of nations will leave a huge void, when people realise the police can not only no longer help them, but may be actively working against their interests. Police may even be incentivised to use their position as "trusted" people in society to raid people's homes.
Quis custodiet ipsos custodes? It's a story as old as time.
Private security will therefore be big business I expect. Crime may well be too. Some of us may not like the idea of living in that world, but it has happened throughout history.
I've seen this vision too. It's always been in the back of my mind when I hear the conversations about getting rid of the state, and how great it will be when its tyranny is finished. What you get in that situation is what you've described here, and what @CheezeGrater described below: a bunch of smaller, individual state-like crime orgs that have state-like powers in the worst sense of the word, and that you get to deal with directly in ways that are generally less pleasant than what you're dealing with now, unless you already live under one of these systems.
"If you liked school, you'll love work," etc.
Then the cycle and human nature repeats. A new flight to self-custody once more.
My take on the cyclical model of history is less crisp than what you've expressed, but there are certainly rhythms to these centralization / decentralization flows. It's hard to see how the current thing doesn't fracture. And then the distinction between crime org and state eventually blurs, and the pirates become captains. People pay their protection money and dream of a more ordered world.
In the meantime, I really hate this kidnapping racket, and would like to route around it.