I like this idea very much. Make water only during the day. Water consumption is highest during the day anyway, and water can be stored much easier than electricity.

I wonder what the amortized cost of solar energy is? It's probably still more expensive than Israel's $6 per million BTU.

In a desert with plentiful sunshine for an application where you don't need to worry about distribution and storage, I would expect solar to be quite competitive with even the notional price of fossil fuel.

When you compare it with the real price of fossil fuel (i.e. add the negative externality of carbon dioxide emission to the notional price), solar wins by a country mile.

Good luck finding water to desalinate in the desert!

Many deserts are within convenient pipeline range of the sea. Including Israel and California, the deserts being discussed here.