Reverse osmosis doesn't require any energy to run it, just have water pumped through the membranes and filters. Probably don't need a nuke plant for that.
Actually, RO requires a LOT of energy to run, because you need some very high pressures to push the water through the membranes.
That being said, one of the advantages of a correctly designed nuclear plant is that you can use the 'waste' heat to distill water. It takes more energy than RO, but only needs it in the form of relatively low grade heat, not electricity or steam for pumps. So it's actually more efficient.
After that, it's just a question of scale. You can run a really small RO system with a hand pump. Supplying a city with water takes more.
That being said, supplying 'the people' with water has never really been an issue - they're willing to pay enough that there are many, many options. It's the farms that are sucking up all the water, and they can't afford the prices for desalinated.
