Is it just me, or did this article dance around the question? I am not a physicist but let me give it a stab: except for a few specialized steps like UV or oxidizing heavy metals, most filtration is mechanical. A series of filters with smaller and smaller pores capture more and more of the mess in the water like bacteria and particulates while UV breaks down viruses, the oxidizer precipitates out metals, and so on. N…
1) There's a large difference in energy and entropy between seawater and drinkable "fresh" water. This represents a bare minimum expenditure, below which you can never go, lest you attempt to create a perpetual motion machine.
2) No matter how you do it: Well, now you have a bunch of previously dissolved solids covering everything. How do you get them off of your surfaces and out of your tubes and "away" from everything else?
Once you stare at the first factor, then look at the second factor, then go back and forth, you come to your senses and realize that the dream of a jeroboam of colorless, tasteless water next to a little pile of fine powder is just not going to happen, and that the more sensible thing is to release some extra briny water back to your source and hope it doesn't kill too many fish.