Scale.
Droughts happen because enormous areas of land lack water. If a hundred million acres need an extra inch of rain, that’s…well, way too much water. In addition, the enormous amount of salt produced by such stations would need to go somewhere, and dumping it back into the oceans would turn them into the Dead Sea before too long.
In addition, desalination is an incredibly energy intense process. You either need to evaporate the water (which, considering the properties of water, is absurdly expensive on that scale), or force it through osmotic filters which cannot be made on that scale using anything like our current infrastructure. I haven’t done the math, but I’m pretty sure even extracting all the energy of a nuclear weapon as heat and using it to boil water with maximum efficiency wouldn’t be enough to do anything like solve a drought.
If we tiled a couple deserts with solar power stations we could probably power such an operation. But at that point we have enough energy to do basically anything else we want to as well.
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