Yes but the risks associated with storing brine are far less than oil. Brine leaks out? It might kill the flora nearby but rain will eventually wash it away. Someone blows up the brine tank? Divert some freshwater until you can rebuild.

But in reality, storing all of that brine would be a massive undertaking on its own. The largest salt cavern is 37M barrels which equates to a circular pond that's 600m across and 20m deep. That's huge. And of course you don't want the brine seeping into the ground water so it needs a good liner. But I suppose you really don't need a pond that big, how often are we completely draining the cavern anyway? We're at half capacity right now and that's the lowest it's been in 50 years. Normally it's been much much higher. So you really don't need all that brine, just enough for the normal ebb and flow of the reserves, maybe like 10%. In the event the reserves get drained, divert some freshwater to compensate.

> as well store the oil in those tanks

Salt does not burn, unlike oil. It would be sufficient to store dry salt, and prepare the brine during the pumping. Still a lot of hassle, of course.

Just spitballing here, can't you just store the salt alone and make the hyper-saturated salt water on the fly? That seems reasonable.

You don't need tanks to store the brine, just a huge pit/pool. If you look at satellite imagery, that giant pit with brine in it is exactly what they have next to the storage facilities.