I imagine that it's not so much the "nuclear ship" part as much as it is the "nuclear merchant ship" part. Of course you can build big nuclear-powered vessels. But how many governments are willing to part with enough uranium to power such a vessel? Civilian use of nuclear material is extremely restricted and enforcement of maritime law is already something of a problem area due to how international the whole thing is.

Well, Russia already operates such fleet and generally considers it as the only feasible way to go with Northern route - to break ice you need a lot of power. I'm pretty sure China won't see a problem with admitting such vessels in their ports or even operating some on their own. With Northern route it's the only way to go in next 50 years, while Arctic is still fully freezing.

The United States did in 1959:

https://en.wikipedia.org/wiki/NS_Savannah