Here's a little of an experience of mine with why I tested my water. When you add corals, they will use up so much calcium, alk etc. The more corals you add, the more the demand will come for these same trace elements to be supplied to the tank. We try to shoot for NSW (atleast I do) because in actuality, we are trying to replicate nature as best we can. So, on the testing, if you don't test for these things and don't have automated dosers, then how will you know if adjustments need to be made in your calcium dosing or alk to keep that proper balance? In my case, I used 2 part B-Ionic to dose. I would end up with an empty bottle of one of them and would still have half a bottle of the other (can't remember which was which). Added more corals, tested my water a few days after and realized I needed to increase some of my doseages to compensate for the increase of calcium and alk uptake. If left alone to run it's course without testing (when dosing or not dosing), at some point I'd imagine that alk, calcium and mag for eg will be all out of whack. Just my opinion though...
As for my thoughts on water changes, I like to do them weekly (10-15%) and the reason why I do it religiously this way is because I have OCD and feel like the more I clean to remove waste, the better my tank will be. I can have this all wrong and could be causing more harm than good but works for me. Don't allow the waste to remain in the tank then no excess nutrients to worry about.
Just my experience though and my 2 cents on it. Keep the feedback coming.