It depends on the source water. I kept my 15 gallon tank with tap water for a year without any problem when I started it. I have a 5 gallon plant refugium on it. The only problem I had during that time was a film of diatom. Tap water in Madison seems to have enough silicate that diatom flourished. When I started using RODI water, my lawnmower blenny lost its food source (diatom and some film algae) and starved to death.
However, tap water seems to vary a lot in quality from time to time and from place to place. I am happy that I switched to RODI water. The tank seems to stay a bit cleaner. You can use tap water, but beware of the problem that it may bring from time to time.
Many utility companies issue annual drink water reports. Have you seen one of these for Cullman? They measure a lot of different things. It's kinda enlightening. However, these reports only show average values including nitrate and phosphate. For example, phosphate and nitrate levels are a lot high during winter months in Madison. EPA allows copper level up to 1 ppm. Madison water is generally below 0.5 ppm on copper, but it can fluctuate up or down periodically. As you know, copper is toxic to inverts and small organisms. An angelfish breeder friend reported losing all new batch of fry to an elevated copper level (above 0.5 ppm but below 1 ppm.) I have lost my daphnia culture completely a few times when I did large water changes (I do water changes routinely), too. I use a certain dechlorinator that detoxifies chloramine, chlorine, ammonia, NOx and other heavy metals, but I suspect that the normal dosage could not bind an excess or something extra in the water. If you see a road construction near your house, watch out. I understand that utility puts extra chlorine in water when the water main breaks during construction.
Is there any reason why you want to stop using RODI? I know it wastes a lot of water, but it also costs a lot to get rid of algae that is often fueled by excess phosphate and nitrate in tap water.