The systems are basic mechanics and break down all the time. Motors, pumps, valves, pipes, etc. They are present and similar in every type of ship engine. Piston, turbine, nuclear.
The difference with nuclear is you can’t have any of the components fail for even a few minutes without absolutely having a redundant backup in place to go online immediately. Redundancy and mission-critical systems multiply the cost of everything in a plant.
There may be a point where is becomes profitable if fuel is extremely expensive but the safety concerns are such that it will likely never be allowed. The government allows private stationary plants but with extreme oversight and multiple extensive security perimeters in reasonably remote areas. Such a thing is not possible on a freighter that travels to major ports around the globe. Only on military vessels with capability to fight back against a military attack is it safe.
There are some inherently safe reactor designs that I am hopeful for but they are still prohibitively expensive and inneficient for private industry.
All “problems” are opportunities waiting solutions and usually when humans put our will to solving them we can. I have confidence that one day we will end debates over carbon, because most of the world will be powered by nuclear in one fashion or another, directly or indirectly.
I agree with most of your post, but when it comes to military ships, I think that it's more of a calculated risk, given that such ships' ultimate intent is to, if necessary, go into harms' way. Of course, the idea is also that "harms' way" not be right on the US coastline!