The (historically) low price of bunker fuel led to the development of turbine locomotives for railroads[1]. The idea was that the low price made up for the inefficiency (in operational practice) of turbine engines. When the plastics industry figured out how to use bunker fuel, turbine locomotives became uneconomic to operate. I'd guess that nuclear cargo ships would simply lead to slightly cheaper plastic.
[1] http://en.wikipedia.org/wiki/Union_Pacific_GTELs