I agree with most of your points, however: most of the accidents have more to do with flaws in regulations than mistakes from the nuclear engineers. Chernobyl, which is arguably the worst and most iconic nuclear disaster of all times was mostly caused by a severe violation of procedures.
When you take into account he amount of energy that has been produced by nuclear power since the 50s, I'd say we have a pretty good record when it comes to overall safety.
The biggest problem with Chernobyl was the reactor design, which had a positive void coefficient, which outside of something like CANDU reactors is considered insane today. It’s true that their experiment with simulated blackout was the proximal cause, but the fact that increased steam production led to higher power output was the big factor that made it such a huge disaster.