The US and Russian Navies deciding to remain mostly petroleum-fueled is one of the strongest arguments against nuclear becoming very cheap: surely they would do it if it wasn't ruinously expensive, because it eliminates the national security risk of a petroleum blockade and simplifies at-sea logistics immediately.

I don't know much about militaries or nuclear reactors, but I know that reactors are used in some submarines and in some aircraft carriers -- situations where you want a vessel to to remain at sea for long periods of time without refueling, and weight is not a primary concern.

That's pretty niche, though. Think about trucks, tanks, aircraft, generators for outposts, etc. It might be cool if you could safely package a zillion nuclear reactors for those use cases, Terminator style, but I'd guess that reactors are a better fit for centralized, permanent power generation.

Don't presume too much about the US Navy's fleet decisions. Using that same logic you could presume that smaller, aged and poorly maintained fleets are advantageous for naval supremacy since that appears to be the choice of the US Navy for a couple generations now.

Or you could presume that the complete inability to build a merchant marine fleet was also a strategic advantage!