At the end of the day, an RO/DI system is about eliminating variables. It's difficult enough to keep a successful reef tank without worrying about your source water changing without notice. To many people, RO/DI is cheap insurance that you know you're starting with the cleanest water possible.
And when I say cheap insurance, I really mean that it is cheap. A 4-stage unit from BRS is $150. After just 200 gallons of water made, your water is only going to be costing you $0.75/gallon. And that includes the cost of waste water. After 500 gallons, your average cost per gallon is about $0.30, and after a thousand gallons of RO/DI water, your average cost per gallon is just over fifteen cents. This doesn't count the cost of replacement filters, but the longer you use the unit, the more it pays for itself.
Consider all the costs that go into a reef tank. Think about the hundreds, sometimes thousands of dollar spent on lighting. Think of the hundreds of dollars spent on tank and stand combos. Think about the hundreds of dollars people spend these days on just one pump. Think of the cost of the sump, as well as the several hundred dollar skimmer in it. Consider the cost of the rock and sand. Consider the expensive fish and corals that we buy. Consider that some people spend a mortgage payment on what is essentially a rhodactis mushroom, or for 3/4" of the Acro of the week. When you add all these up, it's not unusual for even a modest reef tank setup to cost at least a thousand (if not several thousand) dollars. That also doesn't count all the intangible costs such as time you spend researching, ordering fish, cleaning the tank and equipment, making saltwater, etc.
Using tap water is a gamble long-term, plain and simple. Tap water quality can change on a dime without notice. Don't believe me? Ask the unfortunate people in Flynt, MI who still don't have clean drinking water today, 4 years after the water crisis began. It doesn't seem like good mathematical sense to put thousands of dollars and potentially hundreds of man (or woman) hours on the line simply to avoid buying a $150 water filter. Our aquariums are more about keeping water than keeping fish or corals. I'm all about being cheap, and I love saving a buck, but I would not cut corners on water quality to save money. I would find another place to cut and save a few dollars.