When I toured the USS Carl Vincent (a nuclear air craft carrier) at Alameda I was surprised at how "small" its engines were relative to large container ships. It helps that they are electric of course (no big gas expansion chambers) but I suspect if it weren't for the proliferation concerns cargo ships of this size could be economically run on nuclear power plants.
Indeed, Nimitz-class carriers have far more powerful engines,[1] as do as do Russian-made icebreakers, which are civilian ships,[2] as did Savannah, an American civilian ship.[3]
Edit: Carl Vinson, like most nuclear-powered vessels to date, is direct-drive. The Ohio Replacement Submarine is slated to have electric drive.[4]