I tried this once. I thought I was being clever. I boiled a kettle, let it cool, and poured it in.
Boiling kills bacteria, sure. That’s good for a few days. But boiling does not remove minerals. They are still in there, waiting to dust your furniture.
Boiled tap water is better than cold tap water if you are in a pinch. But it is not a permanent solution.
You are just making hot, sterile, mineral-filled water. It’s a half-measure. Go for the full win with distilled.