I owned a full line pet store for over a decade and attended many seminars and trade shows and these were some of the points emphasized :
Once the water is distilled it will contain no beneficial minerals or salts, it is alright to use this water when topping up the aquarium to compensate for evaporation losses but do not use this pure water for water changes or for filling the tank.
Distilled water will have a very low oxygen content, before using this water it must be aerated for a couple of hours or leave it for 24 hours standing in a suitable container to allow gaseous exchange.
The buffering capacity of distilled water is very low, it will need a buffering agent added back to the water to increase the
KH so that there is no chance of any pH swings in the tank.
Ph and Dkh play a vital role in coral skeletal regeneration and health and you can and will read of Many on here who use various forms of water and other than for top off, distilled is the most low use type of water.