Salts don't leech nutrients, but water. But then water is also a nutrient, aside other things. We definitely don't need salts, but we do need minerals. Salts are made of minerals.
To get minerals from salts salts need to be in water solution, as they go into ionic form.
If you ingest just pure salt, water is needed to neutralize it's toxic and harmful effect, by converting it into ions which the body can use easily. So water from the body will be directed toward the ingested salt, leeching it from elsewhere.
When the body becomes deficient of water (at least in some parts of the body), as there's excess salts to deal with, nothing can work right. For well-working metabolism the most important nutrient is in fact water itself. Nothing, absolutely nothing, can work right if there's too little water (and not just water, as water also has to be structured right...). Water directed elsewhere, too little for well-working metabolism, so it will seem as if nutrient deficiency when in fact nutrients are all there, but what's missing is the necessary amount of correctly structured water for the nutrients to do their job.
Since water is sent to deal with excess salt, that salt along with the water is expelled from the body, as water also serves as a medium of transport.
So here's two or three ways for the same/similar effects. Deficiency of correctly structured water necessary for nutrients to do their job, or the deficiency of nutrients themselves, or both together.
I suppose similar applies to excess minerals as well.
