Gets rid of chlorine but not chloramine which a lot of places use instead of chlorine. All the other minerals in the tap water are still there and 90% of the pH and other problems I've seen over the years are water quality related.
For the RO I use since my distiller died and the distilled water when I had it I keep a 5 gal jug handy with a small airstone bubbling all the time so when I water my plants I know it's full charged with O2. Not important with the DWC as the stones in the tub will charge it up fast.
You should also contact your city to get a copy of their water analysis. Should be free and they can likely email it to you. Post it up here or copy/paste it in a PM to me and I'll let you know what's in there for ya and what to watch out for.
Minerals in your water will build up in the soil then pH is impossible to control and all the extra Ca and Mg, which hard water has lots of, will lock out other nutes like P and K. Could be high in sodium, iron, manganese etc but you won't know until you get a report.
Anything over 150ppm or so will eventually cause problems.
