I love the theory, but the security concerns around nuclear anything are a big deal when we're talking ships that sail around the world.
Imagine if even one of the tankers hit in the strait of Hormuz was nuclear.
Would Iran be as likely to have hit one of these ships if the result was potentially a nuclear meltdown close to their shoreline? It would pretty radically change the costs to them for such an attack, wouldn't it?
It would have sunk to the bottom and been of no immediate concern. The benefit of nuclear reactors on boats is that you can drown it out at anytime. The only real concern is a nuclear ship getting beached and not having the passive failsafe of sinking underwater.