I was thinking of getting a distiller until I read that completely neutral water drags in carbon dioxide extremely quickly and this makes the pH of the water very acidic (commonly about 5). Isn't it likely that over-acidity of the water supply is part of the health problem?
there are mineral waters with pH's which are much more alkaline due to the mineral content, and volvic for example contains silica which apparently helps to chelate aluminum, which is a major water contaminant.
volvic pH is 7 and evian is 7.18 I believe. It's expensive though I know.