They have done. The Three Mile Island accident happened when it was being operated by Navy vets [1]. Simple training isn’t enough.

During the investigation of the accident the Admiral that built and ran the Navy nuclear program was asked how the Navy had managed to operate accident free, and what others could learn. This was his response:

> Over the years, many people have asked me how I run the Naval Reactors Program, so that they might find some benefit for their own work. I am always chagrined at the tendency of people to expect that I have a simple, easy gimmick that makes my program function. Any successful program functions as an integrated whole of many factors. Trying to select one aspect as the key one will not work. Each element depends on all the others.

So recreating that accident free operating environment requires a lot more than just training. It would require wholesale adoption of the Navy’s approach across the entire industry. Which probably doesn’t scale very well. Not to mention the Navy operates much smaller nuclear reactors compared to utility scale reactors, and has extremely easy access to lots of cooling water, which probably gives them a little more wiggle room when dealing unexpected reactor behaviour.

[1] https://jackdevanney.substack.com/p/tmi-lessons-what-was-lea...

Would it be fair to say that because the US Navy is not running it as a for-profit power generation that would help. Like every accident seems to be a list of cost saving shortcuts being responsible

Their safety record is good, but can they generate power at a cost that's commercially competitive? If it's too expensive then the plan doesn't work.