https://en.wikipedia.org/wiki/NS_Savannah
The US had a nuclear powered cargo ship in the 1950s the NS Savannah. Operation costs as well as non proliferation concerns ultimately was its down fall. It is clear that the CCP does not share in these concerns. The US has and has had the technology to compete the question is one of will. Will the US in light of China start to see its own nuclear merchant fleet? The American Bureau of Shipping (eagle.org) https://ww2.eagle.org/en/innovation-and-technology/technology-advancements/nuclear-energy.html has plans if the regulators will allow it.
https://www.nationalgeographic.com/history/article/nuclear-ship-savannah-atoms-for-peace