O.k. I disagree On Ro/DI water being necessary. I have a friend that's been into reef tanks since '99. And has used RO water the entire time (No DI) and he has advised me to not worry about RODI water. It's overkill. I'm not saying any one person is right or wrong..
I agree that RODI water will increase the potential for a tank and decrease the chances of things going south quickly. I totally agree it eliminates uncertainties. After all, if water has 25 TDS, we don't know if that 25 TDS is sediment or Copper. So, I agree, RODI eliminates the uncertainties.
With that said, a water softner / RO filtration system combination should eliminate a majority if not all heavy metals from the water. Leaving nasty things like phosphates as possible pollutants of a tank.
Either heavy macro or additional filtration to remove phosphates and carbon to remove anything else is probably a necessity. With that all said. I believe water changes can be done with RO water and the tank be successful and full of life and longevity. Tap water? I agree, Tap water should just be avoided. It has the most risk of pollutants getting into the tank as cities change their treatment plans, so too may water have additional polutants, fleuride, and other chemicals that could be detrimental to a reef. Can it be done. I'm sure people have done it for years. The chances of success for more than 1 year? Hard to say.. Depends on what's in the tap water.
As far as water changes, I read an article on water changes from Randy Holmes-Farley. There are 2 major reasons to do water changes. If you're not doing this or have other methods to do this, then water changes may not be necessary:
1. To remove waste / excess nutrients from the tank.
2. To add minerals essential to a coral reef. (alk, ca, magnesium, strontium, ph buffers, etc, etc).
To oversimplify: To take something out and / or to add something to the existing water.
If there's otherways of doing these two things, then, theoretically water changes aren't needed as much. The person I bought my live rock from hadn't done a single water change for a over a year. The corals and fish were doing good.
He had a huge refugium full of macro algae, and he ran a skimmer. (Huge being 50g +... I have a 14g sump , so 50g sump would be huge to me.

)
I think it best to do water changes, just a matter of how often... And that depends on a ton of variables.