Earlier quoted context omitted.
Capital costs vs. marginal costs. You're going to build a $100M desalination plant and run it for three hours a day? That's a ton of money sitting idle most of the day, far more than what is recovered with zero operating costs. (This is called the utilization factor -- how long a piece of equipment is used vs. staying idle) Ideally you want useful processes with low capital costs and expensive marginal/energy costs.…
Desalinization isn't a good example for the reasons you say, but theptip writes below that heating water in residential and commercial settings might be better. Since water once heated stays hot for a good while in the insulated storage tank. Also buildings can be heated with hot water instead of forced air, typically through pipes in the floor. Which is nicer because it keeps your feet toasty and doesn't dry out the…
They already work on this principle, more or less: heat up overnight when electricity is metered cheaper, then discharge during the day.
There are several companies working on making "smarter" versions that can switch on and off in response to real time data.