Minerals are solid, they don't evaporate.
Many chemicals will evaporate, but also many will stay. Most chlorine now is actually chloramine which does not boil out....though 99% of the population still believes it's still chlorine. It will even stay in the water for days and I've seen even weeks and it's as strong as it was coming out of the tap.
Metals also won't evaporate.
Boiling the water is to kill bacteria primarily, it doesn't remove anything else. Even the bacteria, the dead bodies will still be left behind.
Distilled and Reverse Osmosis are the only ways to get water pure.