I only have a BS in Physics but you're basically correct. But to make it even more simple and divorced from method:
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.
A sensible thing to do is to turn the waste brine water into a resource. Since it's already been pumped up, pour it out into an evaporation pond to increase humidity in an area that could benefit from it, and then scoop up the salt to extract valuable minerals.
I guess there aren't that many valuable minerals in seawater.
For example, Fritz Haber, a German Nobel Prize winner in chemistry, tried to extract gold from seawater after WWI to pay for the war reparations... long story short, the concentration of gold in seawater is too small.
Also, the phase transition for H2O from liquid to gas requires a lot of energy and space (evaporation surface). In other words, it takes ages to evaporate all the water. Also, the larger your pond is, the more expensive it is to scoop up the salt. And then just one rainy afternoon can set you back a lot.
Really good question! The answer is: it's complicated.
When you dissolve a "salt" (the whole class of them, rather than just NaCl), there is a lattice energy (you are tearing these crystals apart) and a hydration energy, which are a little give and take from an energy standpoint. Most salts dissolving are slightly exothermic. NaCl dissolving is very slightly endothermic.
Seawater? Well, remember, there's a lot of dissolved solids in there, not just salts. So you have a summation of dissolving a whole menagerie of different things into your water. Last I heard, and it's been many years since I went near anything like that, yes, there's both an entropy and an energy cost, although I would personally dread trying to do calorimeter measurements to verify it experimentally.
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.