Aloe vera as Nick mentioned is one problem (this has been shown to affect fish gills long-term, plus it messes with the tank's biological system). As for what is might do to help fish settle in...that is highly debatable. There is no doubt that fish can settle in as well if not better without it.
Which brings me to the main point of my post. The fewer additives/substances added to the water in an aquarium with fish, the better the fish will be, meaning less stressed and healthier. Fish have a very unique relationship with the water they live in; 80% of a fish is water, and this water is separated from the water the fish lives in by a permeable membrane, thee cell. Water is continually passing through into the fish, along with any substances in the water; these enter the fish's bloodstream and thus get to the organs. Something similar happens in the gills. The fewer additives in thee water, the less chemical stuff inside the fish to hamper its physiology and metabolism.
With that understanding, additives should only be what is absolutely essential. If we use tap water with chlorine, we must use a dechlorinator. But beyond this, unless there is some specific problem requiring additives or medications, leave them out.
You Tetra AquaSafe is a dechlorinator. I cannot seem to track down exactly what is in it, and this annoys me as I like to know what I am putting in the water. But from the description, it seems to be OK. It dechlorinates, detoxifies heavy metals, and adds vitamins--none of this is bad.
Tetra SafeStart is OK initially, as it adds beneficial nitrifying bacteria. But once the tank is cycled and has fish in it, I don't see a need to continue this product.
The StressCoat we already determined is not beneficial, and somewhat the opposite.
Clean water, achieved by not overstocking, not overfeeding, not using unnecessary additives, and weekly partial water changes of a good volume, is what fish need to be healthy.
Byron.