The point of a water changer isn't to make starting water movement easier, but to continue water movement even if you can't use gravity to keep it going.
I, for one, live in an apartment and don't have a garden hose. Or a garden.
While this is true, there are two things wrong with this. 1) Tap water is often colder than rain water, and 2) The water added in a water change is relatively speaking much greater than the water added during rain. We're talking 5-10% over the course of hours vs 10-50% over the course of minutes. It's potentially unsafe.
1) Not necessarily bad, and very unlikely. If you have this, then you probably know about it.
2) All water will have minerals in it, assuming it has the same source (and they generally do)
3) It's fine to drink. I make coffee out of that water. I bathe in that water.