Yes, Simon. If by using RO/Distilled (or, as you have, "Zerowater"), you know exactly what is in your water when you add minerals back in.
Tap water could have chlorine, chloramines, pesticides, flouride, copper, fertilizers or who knows what else. You can get the water tested to know exactly what's in it, but you're kind of better off just going the RO route and not having to question if the tap changes due to seasons or whatever chemicals are used or what have you. Even if you are living on a well, it's not guaranteed better than city water because it could still fluctuate or get contaminated by something. One person mentioned that they lived on a farm and had well water. Neighbor up the way used fertilizers or something on their property. It contaminated the water system and their tank crashed...