To the OP, what you need to realize is water conditioners do not remove anything. Most neutralize the chlorine and some such as Prime bind some substances so they are not as toxic. They are still there but in a less toxic form and are still accumulating over time.
We all start out with a fish only system at one time or another then we slowly start upgrading to a reef tank. When you have used conditioned tap water you will have lots of undesirable contaminants in not only the water but also in the porous live rock and substrate. These things never ever go away, even in the water it is mathmatically impossible to do enough water changes to ever remove it all. Some things such as phosphates and silicates can really cause problems down the road and give you all kinds of fits and "uglies". You will fight algaes or all types and colors almost guaranteed.
Something I have heard over and over is, "If it is worth doing, it is worth doing right the first time". That really rings true in the reef hobby. I can look back at the last 35 years and count the many different skimmers I bought, or pumps or lights. All seeming like a good deal at the time but none really performed as they could or should. I was trying to take the cheap way out, or at least being thrifty. The thing is, I spent much more replacing and upgradin than if I had just bit the bullet, saved up for the better product in the beginning and done it once. This really applies to water quality in an aquarium, be it fish or coral. Water is the single largest ingredient in an aquarium and everything depends on its quality AND its stability. Tap water changes. What happens when a big storm blows through and the treatment plant has to change their chemical additions and treatment methods to keep up with it? Or Joe Contractor digs up the water main down the block and causes a cross connection when your neighbor has his garden hose stuck in a tree well or watering his garden and it sucks the fertilizers and dirt back into the water main? Or when the fire hydrant on the corner gets hit by a car and knocked off and they have to shut down the distribution system causing low pressures and reversal of flows then don't get it well flushed when it is turned back on? Or when your water utility changes their residual disinfectant from free chlorine to chloramines, they don't have to notify you of this.
The thing is, you have zero control over tap water quality and a conditioner is not going to fix it. When you use distilled water or RO/DI you have ultimate control over your water quality. When you add your salt mix you get the very best product since salts are designed to be used with 0 TDS water and your calcium, alkalinity and other parameters are controlled. You are not building up contaminants that cannot be removed by water changes and you are not getting things out of whack with hard tap water that may already have high calcium or may contain copper, phosphates, silicates, nitrates, ammonia. You don't know what is in your water so you really don't want to put it in your tank. Fish are higher life forms than corals so they deserve good wate rquality just as much if not more. Sure, we have all done it at some time or another but we also learned from our mistakes or at least now realize there are better ways to do things. Can you use conditioned tap water, yes, should you, no and for the reasons above as well as those found in many many articles on all the reef forums.