And as far as I can tell, none if those nuclear reactors have been leaking radioactive material. The fact that close to a dozen nuclear power plants have been sent to the bottom of the ocean and have maintained their integrity is testament to just how safe nuclear power is when implemented correctly.
These subs are continuously monitored. Articles on the internet say Kursk had a minor leak that was quickly repaired, without coming close to any health concerns.
Remember nuclear pressure vessels are subject to some of the most harsh conditions when in operation. They're built to withstand contact with extremely hot water under pressure. Will salt water eventually corrode through it? Maybe. But remember energy through fossil fuels and organic matter kill 3 and 4 million people per year respectively. Those concerned with nuclear safety often fall into the fallacy of letting perfect be the enemy of good. The best solution is the least-bad solution.
Keep in mind we've also blown up 500+ nuclear bombs including almost 10 underwater. Not a great idea in hindsight, but overall we didn't experience any major problems as a result.
Seems like even in the worst and extremely unlikely scenario of full detonation, we'd still be fine.
The difference is that those tests were done on or near land, the fallout settled either on land or in shallow water, close to marine life.
The explosions which happened in deep water (Wigwam in 1955 for instance) had practically zero lasting effects beyond radioactive steam entering the atmosphere.
The scale is a little different though. Say a 300MW submarine reactor runs for 10 years, the energy produced is about 20 megatons. The energy in a bomb might be 400 kt, half of it from fission, so the reactor will contain a hundred times more spent fuel.
