So I just went through this same thing with the aquarium salts for freshwater tanks. The best reason that I read for why to add the salt to a freshwater aquarium was to help with oxygen exchange at the gills, this is also what it says on the box as well. API doesn't specify what type of salt it uses for this product, so I would assume just NaCl. I used it for several months, and did not notice any benefits or harm. I quit using it, and did not notice any benefit or harm.
I believe that any benefits to adding the aquarium salt, if existent, are negligible. Some fish, including some of the ones you mentioned are said to be particularly sensitive to salty water (in the brackish sense). The aquarium salt probably wont hurt them, but if it hurt anything in your tank, it would be them. The one difference that I did notice when I quite using salt was this: I have one single neon tetra, he's one of the first fish I ever bought. The rest of his school died in a horrible fertilizer accident when I was hungover. So he's a pretty shell shocked guy, all alone, and who knows what all that fertilizer did to him. Anyhow, he mostly chills in one spot kinda in the middle of the tank, with a thousand yard stare, and twitching. When I quit using salt, he started exploring the tank a bit more.
Take that for what you will.
Stable water parameters over everything else