It turns out dish towels loop very conveniently from the rack sideways, and it's great for separating and drying the different washing-up rags. This way, too, we can keep the freshest, driest towel beneath the sink for our hands, and leave freshly rinsed towels out to dry above.
We didn't want to remove the rack entirely because we rent and it's mounted really firmly in there, but it seemed too convenient to go unused at all. We're curious though, if anyone would do something different with the empty rack. Ideas?