That's the motivation behind small nuclear reactors (SMRs). Compared to the larger models, these are more "set it and forget it" type of systems, and with it comes the ability to build them much more rapidly than a traditional plant. Check out NuScale Power's VOYGR SMR, as they are pretty far along in the process.
NuScale is cool, but their reactors don't float. Floating is necessary so anyone can just order one and get it shipped, just by pressing a button on their website. And building on land requires all kinds of permissions.
Most of the world is landlocked, besides, you're not going to dock your precious nuclear plant in the middle of a busy harbor one accident, tsunami or other event away from a serious problem. Big reactors have both an efficiency and a security benefit over smaller ones.
But they're still not cost effective which is why the biggest question with nuclear plants always is 'how much subsidy can we get'.
Tsunamis are chaotic in nature, you can't really know ahead of time what kind of Tsunami's are possible just like we don't really have upper limits on what ocean waves can be like. All we have is evidence from those events that we've observed. The ocean is an incredibly destructive environment, hard to appreciate from a land based perspective. Ships are basically in continuous maintenance to keep them working and anything that isn't made of a rust proof material is in for a very rough time.
Reactors on various vessels have entirely different working parameters from those on shore and there the consumer is right next to the reactor. But in the case that you sketch you'd have a floating reactor tied to a stationary power grid that somehow is resilient to the worst that the ocean can throw at it. I just can't see that working, even in the short term, let alone over the service life of a typical nuclear reactor.
Ship-borne nuclear reactors have been used for emergency power, but that's not a structural solution and it is also a very expensive one (compared to land based generation that power is quite expensive). So as soon as possible the emergency use is discontinued and it's back to land based solutions.
Off-shore windpower shows the complexity of ocean based power generation quite well and they have a much simpler safety situation, maintenance schedule, degree of complexity and so on. And even there the challenges are far more serious than the land based equivalent.
But the economics are not comparable to those of anchored turbines (either off-shore on on-shore). Likely something similar would hold for nuclear power, that off-shore nuclear power would by default be far more expensive than on-shore nuclear power and that is already economically not feasible without massive subsidies.
I know very little about nuclear plants, but ignoring the usual risks, could it be anchored to the sea floor? Is the floating element necessary? Would there be cooling advantages also?
