Distilled water is basically freed from what you don’t want to have in your baths: rust particles, chlorine, fluorine (yes, they poured sodium fluoride into our drinking water until 2003), algae, bacteria, sand, chalk, other debris. Not air, because there is a constant spontaneous dissolve of air in water. You make concentrates for your baths with distilled water.
Water from a synthetic resin filter is best for diluting concentrates. Towards the end of your processes you can use tap water, if you add a shot of an organic acid to the final rinse water, acetic acid or citric acid or formic acid (the best but also the most expensive).
I have prepared and used baths with tap water. There is an advantage of tap water for a developing bath, namely that the chalk binds the silver precipitate. Never forget: The light sensitive silver salts struck by light (exposure) decompose in the very instant. Silver remains in the gelatine but the now free bromine (about 80 percent of the silver salts is silver bromide) evaporates. You can smell it when you open your camera.
The evaporation of bromine continues and is boosted up in the developing bath. More silver salts are dissolved out of the film. Chalk, CaCO3, is hardly dissolved in the water. It begins to dissolve upon the presence of proton donators (acids). I mean, with the old-fashioned acid developer recipes that works. With the modern alkaline developers chalk is a nuisance. So, in general, we can use tap water for acid baths but need pure water for alkaline baths. We must ponder cost and income.
