You understand that insurance is inherently fraudulent, right? It can't exist without force, fraud, and eventual state backing. If you pay for Bitcoin "insurance", the insurer is going to use your payments to set up ways to track you and all of your transactions. You understand that, right?
I mean, people here just got done losing a whole bunch of Bitcoins in a fairly obvious ponzi scheme, so I feel obligated to point this out.
HuH? How is insurance inherently fraudulent? Yes, many insurance companies are the scum of the Earth because states let them get away with a lot of bullshit, but that doesn't mean it is inherently fraudulent.
Basically, in the long run it is impossible to both cover worst-case losses
and turn a profit. The only way it works in the real world is via the fraud of fiat currency and the force of government backing. Bitcoin has neither, thankfully.
For insurance companies with incapable underwriters, sure. But as kjj points out, insurance is not inherently tied to fiat, and doesn't inherently fail. In the present environment, a number of the big guys clearly rely on government, but that doesn't have to be the case. Berkshire Hathaway comes to mind as an example of a substantial long-term independently viable insurance company.
For what it's worth, in a bitcoin world, better consumers would yield good insurance companies. Consumers should demand insurance companies that don't write stupid policies, and vote by refusing to give business to the undisciplined insurers.
A lot of this idealism relies on better consumers (more rational demand incentivizing better business behavior). In the current environment where most people expect to be taken care of by someone else (particularly government), consumers have little incentive to be discerning, so the system is broken. In a world without handouts and bailouts, would consumers be materially better; enough to generate a more disciplined, sensible business environment? I think it's an open question.