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By "battery" here, I just mean a dam that holds a few days worth of fresh water.

I think you misunderstood the comment. I agree there has to be a buffer somewhere. You're arguing that we can get a free buffer by piping the water behind a reservoir, but the cost is that the very capital-expensive desalination plant will be idle half of the time. I'm proposing that the more economical option is to buy a lithium ion battery to buffer the renewables and run the desal plant 24/7. (You can still pipe the water behind a reservoir if you want)

I see. It's better to have a half as big plant running 24/7 with a battery.

Thanks for educating me!

Even with battery degradation?

See: collapsing European industry, finally now even in Germany, due to thinking "demand-side response" was a good solution.

This right here. Even low grade continual energy supply is better for desal.