My understanding is that the choice to use distilled water depends on your tap water supply, as far as hard, soft, mineral laden or relatively pure. Boiling your water is not going to change the mineral content appreciably, and in fact when you boil off some water you're actually increasing the mineral content.
Boiling might kill any bacteria or other live pathogens, but the lye will do that just as well IMO, and when you add lye the water goes to 180°-200° anyway which should accomplish about the same. I doubt boiling your water could have any beneficial effect on your soap.
I started with distilled water but when I run out I'm going to try tap water. I wanted to take the least risks and short cuts in making my initial batches of soap so that I would have the best chance at having good results, so now I have the experience to change the water and judge for myself whether the tap water had any negative impact. My tap water here in the San Fernando Valley is practically pure snowmelt water coming from the High Sierra Mountains 300 miles north of LA, and is rated as some of the best quality water in the nation. (Note that the rest of LA does not share this fine distinction.) I'll be astonished if my tap water isn't good enough to make soap. I'm switching as soon as I run out of my initial gallon of distilled water.
If you've been using tap water with good results I see no reason to change.