The problem with nuclear is almost always cost cutting.
US Navy operates with highly trained crewmen and strict discipline. Constant scheduled preventative maintenance. Anyone fucks up gets the boot.
Private operators start off like that. At first they have real engineers 24/7. Then it’s only on day shift. The engineer is replaced with a community college guy for less money. Then it’s a grade 12 guy who takes a week long company course.
Throw in union protection for guys who fuck up. Staff gets less competent and less disciplined as time goes by. A billion dollar facility trying to save a dollar an hour on an employee and saving by cutting maintenance.
As you say, the problem is the difference between what they ought to do and what they actually do. Safety culture has to be built in from the design phase, through operation, right down to final disposal, and that runs up against all sorts of human factors which will try to water it down.
Chernobyl demonstrated that in oppressive places like the USSR, where people were given objectives that were impossible to meet safely and punished for any perception of failure, that the problems went unresolved and even multiplies - there was simply too much pressure to not admit to problems instead of dealing with them.
But where their society's problem was fear (and official secrecy), ours is greed and complacency (and official secrecy).
Navies have had nuclear accidents too - and they use weapons-grade stuff for their reactors, AFAIK. Discipline has sometimes failed, incompetence reared its ugly head as US Navy ships have crashed into each other or subs have surfaced underneath fishing boats etc.
In the civilian world, you have examples like the Mt. Polley mine disaster here in BC - the company was told dozens of times by safety authorities not to overfill their tailings dam or it would collapse, but they did so anyways to save money; instead of forcing them to smarten up, the pols told the safety authority to back off and stop imposing "red tape". result: Collapse, disaster, and millions of tons of pollution flooding downstream. The company still gets to operate, when really their executives should have been hung on a meat hook. Greed wins every time. Same goes for the BP oil spill disaster in the Gulf Of Mexico. Lack of safety flowed from greed, then after the disaster, lack of punishment for those responsible. NASA's Challenger disaster - yes, more "cost savings" pressures to blame, but what is amazing is how an organization that has such a culture of being the "best and brightest" with intense safety engineering and risk management still managed to fuck it up.
Fukushima's the obvious stunning failure in the capitalist world - how did the most earthquake-prepared country on earth, with a strong & innovative engineering culture, never realize that a tsunami could wash its critical backup power connections away? It's like the bosses at TEPCO simply declared that such a disaster couldn't happen and that was that. They had decades to fix this problem, but there too, they just let it go on until disaster struck, and even afterwards were in total denial that the nuclear disaster was taking place. It's as if they would rather die than admit failure.
Sometimes too, there is simply the aspect of corporate & government culture that blinds itself by only wanting to put forward a positive image, refuses to take safety concerns as anything other than naysaying, and fears scandal or embarrassment to the degree that they will ignore problems that are clearly pointed out just to hang onto the [unrealistic] image of being problem free. They will fight tooth and nail to make sure the dangers and dirty secrets never get public scrutiny.
It is no accident that environmentalists have fought against the nuclear industry for so long. Aside from its strong ties to nuclear warfare, it doesn't have a great record when it comes to honesty, have been caught cutting corners many times, has always treated environmental considerations as unimportant, downplayed risks (short term from operations and long term from waste), and repeatedly hides behind the excuse of national security when it comes to public oversight. Indeed, environmentalist experts on the subject are often way more knowledgeable than the average politician who supports it.
It is a tough issue for environmental groups, too - opposing nuclear power means taking off the table a very promising source of energy at a time when energy is needed that doesn't create carbon-emissions. Within their ranks, there is quite a heated debate on this, but it still comes down to two things: risk and trust.
Yes, in theory nuclear power should be well-managed and minimize risk; in practice, it is still subject to the same human & systemic failings as other industries - only while handling something so deadly serious that there is really no room for the usual fuck ups.
Honestly, I worry more about the proposed new "small modular reactors" that are being touted as an lower cost & more decentralized alternative to big nuclear power plants.
At least with the big reactor complexes in Canada, they require a strong base of professionalism, and are an already- known factor in terms of operational culture.
With the small reactors, the boosterism I see makes me think that the sales pitch for it will overwhelm the safety concerns, and we'll end up with dozens of small reactors out in the boonies that are being operated in some half-assed unsafe manner, by people who (as you said) are cheapskates & barely trained at all.