> if an organisation claims to be more competent than the Japanese and and safety-minded too, why can't it persuade an insurer to sell it liability insurance on normal commercial terms, at a justifiable price?
It's because nobody else buys that amount of insurance. A hundred billion dollar insurance policy has significant risks and costs to the insurer completely independent of the actual risk of a claim.
For one thing, the insurer is required to hold enough capital to pay out possible claims no matter how unlikely they are. So you're basically paying interest on that sum of money in the difference between the ordinary market rate of return and the lower return on the "safe" securities insurers are allowed to hold. That cost is completely independent of the risk of a claim; it's strictly based on the amount of insurance you want.
Then what happens if there is e.g. a major earthquake which causes a minor incident at a nuclear plant, so that 99% of the damage is caused by the earthquake but the insurer is a deep pocket and the judge is sympathetic to the earthquake victims? That's a risk an insurer has to account for, but it's not a risk you can address by improving the safety of the nuclear plant because the risk is rooted in politics.
When the risk of an incident is low enough, it's costs like that which dominate the premium for the policy. You can make the risk of a legitimate claim arbitrarily small and those costs would still be the same.
And it's an isolated demand for rigor. Nobody else is required to carry that amount of insurance. When a coal mine turns an entire town into a superfund site and kills thousands of people, they just file for bankruptcy. What would the alternatives cost if they had to carry the same insurance, or pay for their externalities?