In Israel, where a lot of drinking water is sourced by reverse osmosis, it appears that the lack of magnesium in drinking water may have increased heart disease:
I have a RO system at home, and it has a remineralizing cartridge attached to it. It's pretty cheap and seems to do its job well, the water contains healthy levels of minerals (I tested it in a lab).
Why isn't Israel doing it at a large scale? It should be pretty straightforward.
I am still highly sceptical about this and feel it is more of a "fear mongering" advertising - that this "remineralizing water" thing only started so that the RO filter businesses could create another source of recurring revenue. I also remember reading some study that said vitamins and minerals are better metabolised by our body as chemical compounds, as found naturally in food, than as individual elements in tablet forms. And that is why pharmaceutical companies have now started offering such compounds too - like Calcium + Zinc + Magnesium etc. Which also suggests that we may be better of with such vitamin and mineral supplements, if really required, than "remineralizing cartridges" which release questionable dosages into the water.
Distilled water lacks even electrolytes like potassium and other minerals your body needs. So you may miss out on a bit of these micronutrients if you drink only the distilled stuff.
Some studies have found a link between drinking water low in calcium and magnesium and tiredness, muscle cramps, weakness, and heart disease. Also, distilled water may not help you stay hydrated as well as other kinds of water.