> If the statistics were so great, insurance for the plant would be cheap. Yet no one will insure a nuclear plant. Why is that? No one wants to take free money?

This is a common trope, but that answer is that insurance companies are required to hold enough capital to pay a claim regardless of what the probability is. So if you want someone to carry a hundred billion dollars worth of insurance, even if the probability of the event was one in a trillion, the insurance would still be prohibitively expensive because you'd have to pay the time value of money on the hundred billion dollars the insurance company has to hold in order to cover a potential claim regardless of whether one ever comes.

This is why the government insurance thing. The federal government is large enough that it isn't necessary to make them hold that much capital in reserve ahead of time in order to trust their ability to pay a claim, which solves the problem.

There is $450m nuclear insurance available on the market. Perhaps you could work out proportional reinsurance using that plus the reactor maker insurance guarantee. Price-Anderson already incentivizes nuclear quite a bit by the US Gov acting as a backer. It doesn't help because nuclear is too risky for the benefit. Same as hydro-electric. Too dangerous for the money.

Reinsurance is a method to pool insurance resources so that a smaller insurance company can assert the ability to cover a hundred billion dollar claim to begin with. It doesn't solve the time value of money issue, it only moves it around.

Carrying that amount of insurance is prohibitively expensive independent of the risk. Require the oil companies to carry enough insurance on every well to cover a claim the size of Deepwater Horizon and see how fast it destroys them.