They're run exclusively by militaries, which have notoriously liberal budgets and conservative operational safety. Shipping merchants reverse both tendencies. Nuclear isn't safe by its nature, nuclear is safe in the right hands and horribly catastrophic otherwise.
It's a big difference whether the boat the reactor is on has guns and is run by a military or whether it's a random private enterprise without guns. You don't want enriched uranium like it's used in nuclear submarines to fall into the wrong hands.
The kind of fissile stuff being proposed for most forward-deployed reactor designs is not useful for weapons. The biggest danger is blowing up the reactor itself, causing it to be a type of dirty-but-conventional bomb, a non-nuclear (fission/fusion) blast.
This is true on average, but of the available nuclear technologies, reactors used on ships and subs have the highest enriched uranium (making them inherently more dangerous just as a target of non nuclear nations). I believe they are also responsible for a large number of accidents, although when those occur, the affected personnel are usually limited to the crew.
That statistic is extremely misleading because it completely ignore systemic risk. And it does not account for environmental damage.
Additionally, it is not based on nuclear reactors on rusty cargo ships run by cash-strapped companies. Those companies are notoriously hiring the cheapest workforce they can find and dodging regulations in any way they can.
And you would trust them never to leak some radioactive coolant in the ocean?