Granted that water changes replenish trace elements, I use water changes as a source to go through the sand + rocks and clean out the detritus, and other buildup that can cause bad nutrients. The thing that I have noticed is that you want a good source of nutrients that are fresher than stuff that is sitting around rotting. Good nutrients like fish poop...
Also, deep sand beds are notorious for turning on a tank. They build up more and more crap until they start releasing it into the tank. I would go with a shallow sand bed and vacuum it regularly.
If you have some points about why you don't like to do water changes, please enlighten us. You made it seem as though you have a strong belief about not doing them, just want to hear your justification before I make alternative suggestions.