Total US salt production is roughly 40 million metric tons (or 40 billion kg) per year.
Let's say we use this process to desalinate water for just 10% LA County's water needs. LA County currently uses 1.5mm acre-feet of water per year. In SI units, this is about 2 trillion liters each year.
There's about 35g of salt in each liter of seawater.
So... at just 10%, we're desalinating about 200 billion liters a year and producing 7 million tons of salt.
If we desalinate for the rest of the state, or the rest of the Southwest, we'll easily be producing more salt each year than all of the mining activity nationwide.
At some point the excess salt will have no buyers, and we will still need to deal with it.
I'm a fan of the simpler approach: Build long-ass pipes out into the ocean, and slowly dilute the brine so that it's not concentrated in any one spot. The total salinity of the entire ocean will not change by any perceptible amount, so long as you don't drop heavy brine in any one spot.
Sorry, forgot to add sources:
Yeah. It may be "simple" but it's not going to be cheap. I still think it'll be cheaper than dedicating huge swaths of coastal land to become brine-drying fields, though.