Let's start with privatizing the risk of it going kaboom. Why do we need red tape that pushes the cleanup costs onto taxpayer shoulders? It's so safe!
Sophisticated private insurers being willing to shoulder the full financial downside of nuclear power plants going fukushima (not < 1% as it is now!) will give everybody confidence that they're not just pushing propaganda exaggerating how safe they are to an unsophisticated public.
Assuming you are correct, there will be less red tape, the sophisticated insurers will happily take on the additional risks and unsophisticated taxpayers dont have to worry about being on the hook for one of those ~$800 billion Fukushima style cleanup events.
I wont hold my breath though.... after all, they know the nuclear industry would stop existing if insurance were actually priced according to the risk even if the consumers of their expensive public relations campaigns dont.