I really dont see how amino acids is any different than feeding other than being a more focused/specific feed. proteins in food are broken down into amino acids for use. all amino acids do is cut out a bunch of the other crap and save the corals from having to break down the proteins into amino acids themselves.
there are a bunch of aquariums being dumped specialized coral food that dont benefit from any additional nutrients and are wasting their money too. I dont think its a amino specific issue, its a nutrient issue. tanks that can use additional nutrients benefit from amino acids period (just like they'd benefit from feeding if that were chosen instead). the proof is in the pudding. those who add aminos and see the difference should do it and those who do it and see no difference are obviously likely just wasting their money.