The trouble is, our society does so much to the water and environmental pollution is always a hazard, it's probably easiest just starting "from scratch", with rain water or distilled water.
I agree, my grandfather lived until age 98 on "running" spring water (which had to have some minerals is it, but the water was not "hard" and left no mineral trace), but those days are long gone. I wouldn't even be surprised now if his old source of spring water isn't even close to as pure as it was in 1985. Back then the population in his small town was low, everything was cleaner, less pollution.