We all know that being bitten by a radioactive spider is highly useful if you wish to become a superhero, because you will acquire the ability to climb walls and spin webs. Being bitten by a radioactive parrotfish, by the same token, would therefore confer all the inherent skills of a parrotfish. Chief among these is an ability to spin a protective cocoon out of your own mucus.
Hmm. Not exactly going to stop bullets, is it? And you'd have to sleep inside the cocoon too – which, if nothing else, puts an original if somewhat quease-making spin on the usual realms of superhero romantic angst ("Darling, we can only be together if you come inside my mucus with me.... hold on a minute, where are you going?").
And outside of mucus-related issues, you'd also have to spend an inordinate amount of time explaining to sidekicks, supervillains, passers-by and almost everyone else that your superhero name wasn't Parrotman or Fishman but Parrotfishman, and that this did not mean that you combined the powers of a parrot and a fish but that a parrotfish was a distinct species with its own unique inherent abilities. And then you'd have to tell them about the mucus.
Even with the prospect of a snazzy blue costume, it's just not worth it, is it.