I don't think unregulated nuclear is a good idea. Safer reactors would require less regulation and you could argue that even for current reactors our regulation is excessive. The bottom line is that efficient regulation is a hard problem and to use nuclear power we need to either solve that problem or endure inefficient regulation.
It's not that simple. Nuclear regulation in the US has turned (similar to the FDA) into an innovation stifling behemoth... It's a lobbying place and a capital sink and has little to do with safety. If it was about safety, they would shut down current reactor designs yesterday and had started working on Thorium alternatives 20 years ago. The youtube link I posted from TEAC7 conference does explain that quite well.
The current regulation has been pretty effective at what it was intended to do: stop the production of nuclear power plants without the politically unpopular attempt to outright ban them.
People saw Chernobyl and said "none of that in my backyard" and successfully managed to write rules so onerous that they're effectively a ban.
Unfortunately, any plans they had for a solar power revolution in the 70s died when the technology turned out to be outrageously expensive and impractical, and we've been stuck burning coal waiting for the technology to catch up. 40 years of filling the atmosphere with greenhouse gasses because of one spectacular failure halfway around the world and one scare in our own country.
Another irony is the fact that all of our current reactors are old designs and less safe than new ones would be if we were allowed to build them.
Of course all of the political pressure has also killed our waste management plan as well, so everybody has to make due with less safe ad-hoc setups on every site.
It's not actually that hard to fix. We know how to regulate large industrial operations that use dangerous substances. The problem is that we don't use those regulations, we use a whole different set of regulations that were created by people whose specific intent was to make construction uneconomical.
Example. One of the problems that have occurred is that the regulations change during construction. You spend a billion dollars on construction and then the regulations change and you have to start over. The simple change that the construction rules a plant is evaluated under are the ones in effect when construction began would solve half the problem in itself.
There's a difference between regulated nuclear and over-regulated nuclear. If you take a look at the regulations around nuclear startup/operation you'll see some of the policies are insane.
Compared to fossil fuels, which has been successfully lobbied to be under-regulated, you'll stark differences. If fossil had to even approach the same safety/environmental rigour of nuclear, fossil fuel market share would drop quickly.