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.
Seems like even in the worst and extremely unlikely scenario of full detonation, we'd still be fine.
Some Marshall Islanders would like a word
The explosions which happened in deep water (Wigwam in 1955 for instance) had practically zero lasting effects beyond radioactive steam entering the atmosphere.
Of the nine sinkings, two were caused by fires, two by explosions of their weapons systems, two by flooding, one by bad weather, and one by scuttling due to a damaged nuclear reactor.
(for those looking, it's to the movie The Hunt for Red October)
School shootings in the USA and ISIS beheadings don't affect my daily life, either.
Typical powerplant reactors operate in the TWs.
Yes, it's 1-2 orders of magnitude.
I think it is extremely irresonsible to build military equipment with nuclear reactors. They are destroyed in conflict, polluting everything.