It takes 3 very difficult achievements to build a nuclear bomb. Access to reactor grade uranium is only one of them.
I'm not sure the dangers of potential proliferation outweigh the tangible deaths per year that result from large ship pollution.
But fission reactors also produce plutonium. Using that is another possibility, but you need very pure Pu239. Once the reactor has been running for over three months you start getting a lot of Pu240, which is a serious contaminant for bomb fuel. Separating those is not currently feasible.
So one expedient for nuclear ships would be to run the reactors a few months in secure conditions before putting them to sea. Reactor-grade plutonium is still rigorously controlled, because it might be possible to make it explode, but nobody has ever done it.
https://www.world-nuclear.org/information-library/nuclear-fu...
The US tested a bomb made from reactor grade Pu in 1962.
> a 1962 US test using UK plutonium from its Magnox reactors had a relatively a high level of Pu-240 but evidently less than ‘reactor grade’ as subsequently defined
That being said, there seems to be "evidence" (maybe more like conclusions that can be drawn from published articles by people with weapons experience etc.) that Pu with almost any isotopic composition can be used to make a usable (as in, very low probability of pre-detonation, low enough radioactivity to not pose a threat to personnel handling it) weapon.
Now, I don't think that terrorist capturing a nuclear powered cargo ship and then making a Pu bomb is a particularly big worry. Making a Pu bomb from spent fuel (whether with weapons grade Pu or reactor grade) requires reprocessing technology (e.g. PUREX) as well as the engineering to create an implosion device, and is probably out of reach for non-state actors.
The worry AFAICS with reactor grade Pu is that an advanced non-weapon state sitting on a big pile of separated reactor grade Pu (cough Japan cough) could relatively quickly (e.g. weeks/months) create a bomb if they so wanted, compared with building weapons grade Pu producing reactors and running them, which would be a several years long project.
https://en.wikipedia.org/wiki/Dirty_bomb
The biggest threat a dirty bomb poses is fear. Meanwhile shipping pollution is estimated to be responsible for hundreds of thousands of deaths every year which we just take as a fact of life.
Burning oil to move goods around the world is not a sustainable long term solution. Nuclear propulsion might be.
The major concerns seem to be hijacking/piracy, clearance to dock at ports, and the general umbrella of proliferation concerns.
They don't want people taking these and using the material for bad things.
If there was a way around that, then maybe they would be economical. The cheap fuel costs in the past made the NS Savannah non-competitive, but I doubt that's true now: https://en.wikipedia.org/wiki/NS_Savannah