Coral produce most aminos on their own. This has been known for a loooong time.
NOAA National Ocean Service Education: Corals
I agree with you. Photosynthesis accounts for 85% of the corals nutrition, when we talk aminos, and feeding, we are trying to supplement the other 15%.
You are absolutely correct with all stated in your post. As mentioned by other posts, the aminos dosing is for low nutrient systems, which is the case in most sps tanks. I have a small tank(20 gal long) with sps, 2 small fish, gfo in a reactor, run carbon and a good cone skimmer rated for 150 gal tanks. I feed very sparingly so my system is a low nutrient system. Most corals do well with good lighting through photosynthesis. Getting a good dial of the other 15 percent could lead to better coloration and growth perhaps. My concern with heavy feeding the fish is that the food will break down and that would take longer giving room for parameters to rise and decrease which is what we wouldn't want. We hope a good skimmer would take care of that but that is not always the case in reality. Aminos are already broken down, ready to be absorbed, and as you add them, they will be brought in to coral tissue in less time. If you dose it sparingly, the larger amount would be consummed for corals and the left over nitrate will be cleaned up(hopefully). Fish food will provide those aminos, but how much to feed is the question. Lots say you must watch and decrease feeding if algae starts growing, but in that case, when you see algae there is an abundance of po4 or nitrates, and that swing is what we don't want with sps.
Click on the PDF on the page to see the article---
Biosynthesis of 'essential' amino acids by scleractinian corals.
Most people that are getting pale or starved corals lack nitrate and phopsphates. Fish food contains all aminos a coral needs or may be missing. The fish pass most phosphate through their systems for the corals and bacteria to take some & nitrates are produced from the normal nitrogen cycle that happens when a fish poops. The corals can eat bacteria that contains the nutrients needed.
Aminos contain nitrogen.............when they break down the nitrogen is released. Amino acid products get away with saying they contain no nitrate are just splitting hairs. The nitrogen is contained in the molecule, so it's not actually nitrate when in the form of an amino. That's why some people get algae if they dose too much amino.
If there was a company that would provide just the four aminos a coral can't produce and list it on the bottle it would make more sense, but they aren't going to do that because you'd be able to get it dirt cheap. I don't now of anywhere you can buy specic aminos, but that's what is needed................not a soup some commercial company produces that boasts thier product contains all of the "essential aminos acids"
Basically if you want to give your corals what they need you can throw in a slurry of fish food or buy aminos. Fish food is cheaper and you know what you are putting in the tank. Commercial amino contents are a mystery and cost more and you will never know for sure if they contain all the aminos that are provided by just having fish in the tank.