The real problem is that a nuclear power plant needs a staff of several hundred people. They can't travel 500 miles every day to work to the middle of a desert. Even if they wanted to relocate there, they would have to build a little town to serve these people and their families, and now we are back to the original problem.
Other problems with building nuclear plants (or any other type of plant that requires large steam turbines) in the desert include:
* Difficulty cooling. If you build next to an ocean or river, you can just use some of that water to provide the cold end of the temperature differential that you're using to generate power. Deserts are trickier, and more expensive.
* Transportation. If you build next to navigable waterways, you can ship really big components on barges. In deserts, you can ship some things by rail.
But hey, at least it's politically convenient to stick scary power plants in deserts.
I'm aware of that, but water isn't the only convenient coolant. Molten salt, sodium, molten lead, and helium are other options.
Water has some disadvantages. It's a good neutron moderator, but with its low boiling point you have to keep it under a lot of pressure (160 atmospheres for most light-water reactors). That means you need very strong, thick steel, and a huge oversize containment dome, since if a pipe breaks, the steam will flash into 1000 times as much volume. Then some of it will split, and you'll be at risk of a hydrogen explosion, which is what we all saw at Fukushima.
Molten salt, on the other hand, works at atmospheric pressure, and if something leaks it just drips out and cools into rock.
Sodium has a disadvantage in being reactive with oxygen and water, but it also works at atmospheric pressure. The integral fast reactor design uses a big pool of sodium, which provides so much thermal inertia that Argonne was able to switch off the cooling system entirely, and the reactor just quietly shut down.
Either design works at higher temperatures than LWRs, giving better thermodynamic efficiency.
