I understand that, but it is kind of interesting. The purified water recovered doesn't disappear from the water cycle, but is used and eventually reenters the cycle at some point, and that would include the oceans. In other words, the water your remove from the ocean eventually finds it's way back.
So, if you don't dispose of the salt and minerals recovered back into the ocean, won't that eventually throw off the salinity of the oceans by making them less salty than they should be?
You’re talking about a very, very gradual return to the oceans and at various points. The current process most often means effectively dumping the brine back into the ocean in one place, vastly increasing local salinity. It takes a long time without further brine dumping for that to dissipate and return to normal conditions. In the meantime, a dead zone has been created where the entire food chain is wiped out. It takes a long time for that to recover and it can only begin that long process after the salinity levels have returned to normal. Which never happens so long as brine is continually dumped back to that point.
Imagine a clear lake that’s pretty large, but still small enough to see across. If you dump a bunch of mud in one part, it’s not clear in that part for a while. If you wait long enough, it’ll clear up again. But if you keep dumping more mud there, it’ll just stay that way indefinitely. As time goes on, if you continue this process, you’ll affected a larger area and more severely affect the local area (perhaps changing the shoreline from mud build-up).
The answer here would be to store the brine and combine it with filtered waste water, then distribute it across a larger area where it rapidly dissipates. This is a more costly way of going about it, but you avoid the destruction of the local area.
In the very long term, you’re right. Earth is a closed system, water and all. But in the shorter term returning the highly concentrated salty sludge to the sea (or wherever) is devastating to the immediate environment.