Desalination plants aren't really something you build for profit, they're to secure your cities clean water supply and are usually taxpayer funded infrastructure projects.
A realistic/feasible deployment would perhaps pair desalination with solar or wind (more likely on the coast). During electricity peak hours, it might be more lucrative to sell electricity to the grid and then the rest of the time top up the reservoir. I guess depending on how scarce water is, the $ per kwh earned via water might actually be larger than selling to the grid. But you get my point.
You are right that these things being funded via tax payer money, makes this kind of lateral thinking less likely. But if someone were to do this commercially, this would be a great way to make it more cost effective.
We need more solutions that work like pumping water back up into a reservoir (see other reply). These solutions aren't at risk that they need to run on high energy cost anyway to stay profitable.