Same with the german nuclear vessel NS Otto Hahn. Was not accepted in ports and got bad cargo choices.
There was never an accident though
www.radiationworks.com/ships/nsottohahn.htm
I used to be mildly anti-nuclear before I joined the Navy. But now I have seen that nuclear power is great when done correctly. All of our submarines and aircraft carriers are powered by nuclear reactors. The main reason that most US Navy capital ships are not nuclear is cost. I definitely agree that having a FoC nuclear powered ship is a horrible idea. 
We would definitely need a rule that any ships converted to nuclear power have to be US Flag and stay US Flag (the law would say that the ship has to be sold or de-comissioned instead of re-flagged). Or at least the flag of a G7 nation. France and the UK also have experience with nuclear powered naval ships.I think it is an excellent idea, but as others have said, the main problem is politics, in terms of people being afraid of nuclear power.
I think the recent trend to start converting ships to natural gas power is definitely a good thing! Greatly reduced CO2, and particulate emissions are eliminated. Hydrogen derived from clean sources (solar, nuclear) would be ideal, but we don’t have a good way to store and transport hydrogen yet. So natural gas or biofuel might be a good bridge until we develop a means to move hydrogen around cheaply and safely. 