I think it's usually because the native ingredients are hard if not impossible to source, so people try to find ingredients that are more easily come by that meet the nutritional need. This is big problem for zoos, with species that have very specific diets, like Panda Bears, need bamboo, or Koalas, need certain species of Gum leaves. Even silk worms, often offered as reptile food, can only survive on mulberry leaves or a paste made from mulberry leaves.. nothing else will do.
Fish, for the most part, are a bit more adaptable, with, I am sure, some notable exceptions. Puffers, I've been told, don't do well on artificial diets and must have live food, especially snails.
So alternate ingredients are chosen either for their similarity to something else the animal would normally consume, or because it is easy or cheap to get.
Heart contains high levels of taurine, an amino acid which is far less plentiful in other protein foods. Cats, as an example, have a high requirement for taurine, so if you make cat food, to keep taurine levels high, you have to use heart, or a taurine supplement. So I wonder if beef heart simply has a good supply of particular amino acids that the fish appear to need.
Egg protein is said to be 'complete' in that it contains all the amino acids human beings need that they cannot synthesize for themselves. But that does not mean it's complete for other animals, but I think they are often used because they help bind ingredients and have this reputation for being a complete protein. Again, that does not mean they are the best thing to use. Many recipes are the result of trial and error by whomever publishes them, and may or may not have the best ingredients. They'll have whatever that person could get, or had on hand, that appeared to work.
I'd want to know how long they'd been feeding a given recipe to a given species, and whether the fish were successfully breeding on the diet, and what the life span was.. among other things. Many diets will sustain a life, but may fall short in many areas in terms of the micro nutrients, which are the vitamins and minerals, and often specific fats, such as Omega 3 fats, or specific amino acid components of proteins. Most of us think of flax seed as a good source of Omega 3s.. but many carnivorous animals can't use plant sourced Omega 3s, and must have animal based ones. Krill oil is the latest popular source for these fats.
Most of the research on piscine diets been done for food fishes that are farmed, and may or may not apply to other fish, but you can extrapolate from them as a start. If Discus are carnivorous fish then a diet suitable for other carnivorous fish might suit them too. It's a huge subject, with so much information that might or might not apply to any given species.
While I don't know for certain, I'd bet water problems related to eggs are because of the fats and sulphur compounds, which are found only in the yolks.. the protein in egg is quite good on it's own. You can buy egg whites in powdered form, which may make it easier to use.