Two points. You have to dump "low temperature" heat somewhere to have a thermodynamic cycle from which you extract energy. In a sub, the only place is the sea.
IIRC the Soviets have used fast reactors in subs, I think with lead or lead/bismuth cooling rather than sodium. I think everyone else uses pressurised water reactors.
While mixing sodium and water is bad news, the death knell for the Dounreay Prototype Fast Reactor was corrosion, more accurately stress corrosion cracking, on the *water* side of the sodium to water heat exchanger where the steam is raised. This is hot, very pure water which poses more materials challenges than the the cold seawater-to-steam condenser.