Let's build nuclear power plants under water!

Let's build nuclear power plants under water!
The whole problem at Fukushima power plant was the shortage of water to cool the nuclear reactors.
If that is the problem why not build the entire power plant under water?
It could be an artificial lake, a natural lake, a river, or at the bottom of the sea.
The advantage of having the plant under water is to ensure the fuel rods are never exposed to air.
If there is a breach of the containment vessel, water from outside would automatically flood the nuclear reactor, making a meltdown impossible.

Nuclear-powered submarine technology could be used for these power plants.