I think it depends on the tank. Depending on the corals, the fish, the food fed to the fish, and what you want to get out of your corals they may benefit from feeding. For example, if you feed something like Rod's food or almost any frozen food to the fish, you are feeding the corals. You may not have added anything to your feeding regimen specifically for the corals, but that doesn't mean they aren't actively feeding on foods going into the tank.
Even if the corals do well without it, some may do even better with some feeding. For example, many LPS will get everything they need without any direct or active feeding on our part, but a little meaty food once a week or so may be appreciated (and even increase growth rate).
I am not saying corals need food, but I wouldn't say none do (or at least not that none would benefit from it).
When feeding I think it is important to feed for the corals. Tossing in a bunch of foods isn't the way to go. For example, if you want to feed SPS you need to choose a food appropriate for them. This would be things like Golden Pearls, frozen oyster eggs, etc. Not mixes with a bunch of other things mixed in that may not be eaten. Or: with LPS it would be more effective to directly feed them, not broadcast feed. I would feed mine 3mm pellets and they loved it.
That said, anything that goes into the tank has to come out. The more you feed the more nutrients you put in, which is more food for algae. Without an effective refugium or water changes the benefits of extra feeding may not be worth the extra nutrient input and actually do more harm in the end.