I think taking a day off from feeding is something more appropriate to carnivores who gorge themselves and then take time to digest their meal.
I keep corydoras and a few other fish who are more opportunistic feeders. They are omnivores that (in their natural habitat) eat a little here and a little there, a little now and a little later on. I wouldn't intentionally let them go a day without eating, although it probably wouldn't hurt them occasionally.
Then there are otos. These little fish have bacteria in their stomachs that must have regular feedings of vegetable matter. If the bacteria aren't fed, they die and as a result the otos can eat, but they will eventually starve. In my otos' tank I keep a constant supply of zucchini or yellow squash so they can eat whenever they like.