Back to fish; the wrong amino acids in any fish will lead to aquarium pollution (extra ammonia) from lack of digestibility and potential renal failure (kidney failure) in the fish.
We also know from studies in human nutrition that certain diets add to inflammation and oxidative stress.
Reference: Do goldfish Have a Stomach; The Fish Vet?
But more importantly, regardless of which side you fall on the issue of whether or not a goldfish has a stomach; What is a fact is that this small or rudimentary goldfish stomach along with their long intestinal tract tends to loose moisture readily because of this small stomach and long intestinal tract.
Admittedly even some of the better brands perform supplementation, but I still would seek a fish food that supplements as little as possible.
In fact there are many otherwise good fish foods on the market that utilize excellent ingredients (especially the newbies in the market), but their failure to optimize ingredients and/or their preparation process often leaves these fish foods lacking, this includes many, if not most, of the popular so-called "quality" fish foods currently on the market.
One similarity is that if too high a protein or the wrong protein diet is fed, the horse may colic, and in goldfish they will build up intestinal gas and infections including of the swim bladder or occasionally dropsy will ensue.
Anytime one feeds fish foods with excess energy levels, this too creates oxidative stress.Where this article differs from most all others is this information and research dates back several decades and ALL recommendations (& fish food developments) are based on this in depth research.This is UNLIKE most articles that are written after so as to support the latest marketing scheme for a premium fish food.Near the end of this article I do discuss some live, frozen and freeze dried foods.Regardless of whether the fish' diet is 100% prepared or prepared that is supplemented with live/frozen (which I have had test fish do very well in controlled tests on 100% prepared foods), you want to seek a fish food that has the lowest amount of supplementation as well as one that is optimized as per energy points, fiber, and proteins to make the food viable diet. Any prepared fish food that has to add vitamin, mineral, and other supplements to bring their food up to higher standards is obviously not providing these via optimal ingredients and/or is cooking them out via the preparation process (such as making flakes or pellets versus crumbles which destroys less of the nutrition value).