The salt you release isn't instantly diluted in the whole ocean and we're speaking, for a plant, of millions cubic meters of salt enriched water per day. The release area is just dying.
I don't doubt there is an effect, but am not convinced that the "release area just dying" is correct.
Brine disposal is indeed a complex issue. Should be noted the above URL is from a desalinization industry proponent so I would say it's probably a little more optimistically biased but it was one of the better summaries I found so it still has value from that perspective. If you do more digging around each of the solutions they discuss you can find more pro's/con's for each and you will quickly find out that it is a pretty significant issue.
I was more thinking of proper studies, such as reviewed in [0], which says in the abstract: "Ecological monitoring studies have found variable effects ranging from no significant impacts to benthic communities, through to widespread alterations to community structure in seagrass, coral reef and soft-sediment ecosystems when discharges are released to poorly flushed environments. In most other cases environmental effects appear to be limited to within 10s of meters of outfalls."
So, impact yes, but "release area is just dying", probably not.
[0] https://www.sciencedirect.com/science/article/abs/pii/S00431...