They do; https://news.ycombinator.com/item?id=49735585

If you're gonna build a bunch of tanks on the surface to store that saturated salt solutions, you might as well store the oil in those tanks. The point of this salt cavern system is how little infrastructure it needs to store the huge volume of liquid.

Seawater is 10% saturated IIRC, so you'd have to make the saturated solution first, and if the easiest way to do that is to dissolve another cavern then using brine doesn't have much of a cost advantage over "use this one until it collapses, then dissolve the rubble or make another."

Hard to find that