Fish don't digest a good portion of the food they eat and that left over food is plenty for the corals. If you are adding food to the tank for the corals you must be specific. All of these mixes you all are mentioning are not even feeding most of the corals by adding them right to the water column. LPS
must be target fed to make a difference. Putting food in the water column misses them completely. Try a test. Pour your food in and watch the coral. You will see if it gets anything.
99.9% will blow right by it.
Small polyp corals will pick up some tiny matter like that of phytoplankton, but again, if you have fish pooping in the water, there is no need.
Just watch your water quality.