Meanwhile, the biggest issue that faces most nuclear plants under emergency conditions â" overheating and potential meltdown, as happened at Fukushima, Chernobyl, and Three Mile Island â" would be virtually impossible at sea."
Simply being at sea doesn't prevent the cooling problem. Remember, Fukushima was right on the ocean. The problem is that the cooling system has to have at least two loops. An internal loop of coolant (usually water, though salt has also been used) actually travels inside the reactor. Consequently it picks up some residual radioactivity from being exposed to all those neutrons flying around. You cannot just use this single loop for cooling, or else you're releasing this radioactive coolant into the environment.
A second external loop of coolant cools the internal loop via a heat exchanger. This external loop picks up nowhere near as much radioactivity, and the coolant (water) is safe to dump back into the environment.
If it were just one loop, you could come up with a clever design using thermal expansion to make the water flow through it to provide passive cooling in the event of a pump failure. But with two loops (and the inner loop being closed), you're pretty much reliant on active pumping to remove heat from the reactor core. The problem at Fukushima was that power to these pumps failed, and backup generators designed specifically to supply power in that scenario were flooded and their fuel source contaminated.
I don't see how putting the plant on a floating platform helps in this scenario, unless you're willing to open up the primary cooling loop to the environment and just dump water straight into the reactor (with the resulting steam carrying both heat and radioactivity out). Which was pretty much what they ended up doing at Fukushima. If they'd done it before the cladding on the fuel rods melted, we'd only be dealing with a small amount of radioactive water (deuterium, tritium, etc) being released into the environment as steam, instead of fission byproducts being directly released. So I don't see how being by vs on the ocean makes any difference for this scenario.
Maybe you could design the steel containment sphere to act as a heat sink, allowing sufficient cooling when submerged? But the containment's primary job is to contain what happens inside. That's why it's a sphere - it encloses the largest volume for the least amount of material and surface area, and its mechanical behavior under stress are very easy to predict. This is precisely the opposite of what you want from a heat sink. You want the most surface area for a given enclosed volume. Which makes me suspect that the steel containment could only operate as a heat sink if you're willing to compromise its protective strength somewhat.
The other problem I see is that putting it out at sea hinders accessibility. Meaning more mundane events like a fire, which are trivial to handle on land, become much more problematic at sea.