The cost of nuclear maintenance would be far too much for any shipping company.
The reason there are few accidents is because the standards for nuclear plant safety are far above any other machines on earth. To weld a single pipe requires certified welders with security clearance, certified materials and multiple tests/inspections by licensed engineers.
It would also be a target for state sponsored terrorists/pirates so security would need to be at a military level.
Until nuclear is made inherently safe and impossible to be used by terrorists, it will never be profitable in private ships. One bad accident can irradiate an entire continent.
“The cost of nuclear maintenance would be far too much for any shipping company.”
Possibly not so. The primary nuclear costs are one time, and yes with SOME higher operational costs, but with long periods before any “refueling”. If those costs are amortized over all the years oil would have had to be purchased - with the generally over time increasing cost of oil - the total costs may not be that much greater in the long run.
As far as pirates and terrorists, try as they might it is most likely they would not get what they were after.