Well, it does result in enriched nuclear material floating all over the ocean, ripe for the taking by pirates or nation-states that we'd rather not have access.
Pirates still seize large merchant ships in Asian and African waters on a monthly basis. There are only a few hundred surface vessels capable of effective anti-piracy patrols worldwide from all navies and coast guards; they can't be everywhere at once.
It's been done, commercially. It's proved noneconomic and technically problematic. Even without economic constraints, the US Navy reserves nuclear propulsion for carriers and submarines. It used to operate nuclear cruisers, but no longer does.
Several commercial nuclear powered ships were built, the Savannah by the US, and single ships by both Germany, the Otto Hahn, and Japan, Mutsu. All proved uneconomical, the Mutsu had major technical issues, and were either scrapped or converted to conventional fossil propulsion.
Among the more pressing problems is the size and loss rate of the civillian cargo fleet. From the United Nations Council on Trade and Development's Review of Maritime Transport: 2014. Total fleet size 47,601 registered ships, totaling 1.68 million deadweight tons. By type and deadweight tonnage:
* Container: 12.8%
* Dry Bulk: 42.9%
* General Cargo: 12.8%
* Oil Tanker: 28.5%
* Other: 11.2%
And those sink. With surprising frequency. From from "Monsterwellen", by Donovan Hohn in Outside magazine:
This is one reason merchant seafaring is still, by some accounts, the world's second-most-dangerous occupation, after commercial fishing. According to Imperial College London, 200 supertankers and container ships have sunk in the past two decades due to weather. Wolfgang Rosenthal, a scientist at the European Space Agency, which studies sea conditions via satellite, estimates that two "large ships" sink every week on average. Most of these, he says, "simply get put down to bad weather.'
Sure we can do it. Use nuclear plants on land to provide power for the synthesis of carbon neutral artificial liquid hydrocarbon fuels, then burn that in ship engines.
Installing nuclear plants in modern civilian ships is a non-starter for safety, security, and cost reasons.
