Or increased premiums, or torture, or whatever. I think the idea is if you don't like what the insurance company uses as a threat of punishment you can just sign a contract with a different one.

At least you have some choice when you choose your insurance! (Unless they outsource it.)

More or less. There are other formulations in which the insurance-function is bundled with other things (membership in an HOA-like structure, other protective services, etc.), but this is a fairly common scheme supported by a lot of anarcho-capitalist types. You can find some academic economic treatment in _The Machinery of Freedom_, by Friedman, and Vernor Vinge (science fiction author) seemed taken with the notion, too. He experimented with it in the _Across Realtime_ stories. Edit: Also Neal Stephenson, sort-of in _Snowcrash_, explicitly in _Diamond Age_.

I strongly dislike the notion because I believe access to justice is a bedrock function of society. But folks who think like me should also think long and hard about how much access "we" (in the US, not speaking for anyone else) have to justice without a big bank account now, and to what extent this would really change much.