From what I have learned is that softening water is fine for using in mechanical usage. With regard to drinking water, water softening is not good, as it removes essential minerals which are beneficial for your body. It might be that the body doesn't get much minerals from water anyway and most is in food, but if you consider water pulls minerals from sources, softened water, like distilled water, is going to pull minerals from your body if drank in high quantities.
UNBALANCING MINERALS - UNBALANCING YOUR BODY
Since distilled water is completely demineralised, adding himalyan pink salt or alternative is atleast going to give you a balanced amount of minerals. With water softening its different, because there is already an unbalanced amount of minerals in it, because extra salt is used. Having read this article, it suggests that excess chloride is created as a result which damages the environment.
I think the most important thing anybody can do is get some tests done on their own body, to find the balance of minerals. Everybody is different, which is why some people do well with distilled water while others don't. Unfortunately our modern doctors don't seem to be spending any time on working out body chemistry to balance excesses or deficiencies. That is why I only use a standard GAC filter for the moment, which removes mostly chlorine and kills bacteria, and maintains most other minerals.
In todays polluted world I think its safer to have a distiller or reverse osmosis unit and then remineralize / realakalise. The only problem is I've tasted distilled water and it taste nasty. It was ok when I added terramin clay and let it sit for 3 days. Maybe in the future I will have a reverse osmosis unit and then let vegetables and or sprouted grains sit in it for a few days before drinking.