The question is too broad.
If you have a predatory fish, you should probably have a good part of the diet feeders. Not saying just feeders, or even over 50% of the diet, but IMO I think it should be in there. If you buy feeders from a fish store, I would say it's probably a bad idea... They keep feeder goldfish packed in aquariums where disease can easily spread.
If you raise the feeders yourself, it's probably pretty healthy and there shouldn't be anything to worry about. As long as you keep the fish healthy they could be fed to the larger fish.
Fish that aren't predatory would probably be much better off with pellets, insects, and worms.