I think the issue is the scale of the operation. It's not that the desert doesn't have the capacity to absorb brine, it's that pumping all that brine into one

I think the issue is the scale of the operation. It's not that the desert doesn't have the capacity to absorb brine, it's that pumping all that brine into one spot creates a local ecological catastrophe. To avoid a concentration of toxins you need to spread it around, which is expensive. My expectation is that the brine will have to go back into the ocean. The deserts a big, but the ocean is bigger. What the paper mentioned in the article points out is that you can't dump this all in one place.