There are several practical problems dumping the brine back in the sea.
If you dump it on a living ecosystem you tend to kill it. Living ecosystems are, unfortunately, concentrated right where we are desalinating and is cheap to dump.
Compounding this problem is that water mixes much more slowly than your intuition suggests. It can stay a coherent mass of high-salt water way longer than you'd think, killing as it goes. This is one of the more surprising things I've learned in the past few years, honestly. Your kitchen-scale-based intuition of how long it takes for liquids of different characteristics to blend together turns out to be way off.
Trying to pipe it away to somewhere where it is less of a problem is expensive.
In the long term just dropping it back into the ocean is not a big deal, but that short term is surprisingly destructive. You'd think you could just drop it in and maybe a few hundred feet from the outlet it would be all dissipated and harmless, but unfortunately the physics don't work out that way.