I've never had a problem keeping angels in large or nano reef tanks, except for a few stubborn pickers, but even then the amount of damage was minimal. Tank is correct in that fish will subside what we call "bad behavior" when they have more food offered to them throughout the day. IME fish can become bored so offering varied foods peaks their activity level and redirects their destructiveness. As long as the food is eaten there shouldn't be any waste. Either way there is an inherant risk in most fish available for purchase in feeding on our "reef."
A reef isn't a reef without an angelfish