Even if distilled water is fine to drink, to me it tastes completely disgusting, and adding salt to it makes it even more disgusting, I actually drank distilled water that I remineralized with salt for 1 whole year, but then I started drinking tap water again and I just couldn't get back into that distilled water thing, the taste makes me wanna puke.
I've been in the mountains lately, and the natural water there is something I'd love to drink everyday, it's just fantastic.