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I'm wondering if this premise is true. There are many superheroes who utilize their own self-built technology (Iron Man, The Atom) or gadgets and Training from Hell (Batman, Green Arrow). And then any Mass Super-Empowering Event is going to produce a lot of good guys and bad guys (not always accidental, but almost always unexpected on the part of the recipients).
That aside, there is Ambition is Evil for the "I want power for power's sake" type. There is also With Great Power Comes Great Responsibility for when a new but goodhearted superhero commits to using their powers for good (but a superpower-seeker could feel this way).
Yeah, the premise isn't always true, though Batman and Green Arrow are Badass Normals, not superpowered. Iron Man did create his Power Armor, but he had the "excuse" or having the power battery on his chest to prevent him from dying. I'm not too familiar with The Atom, though, so he might fit the idea more.
What I meant more is, if an accident gives a hero superpowers, attempts to "recreate" the accident will only be made by would-be villains.
It seems like superhero stories usually have the heroes get their powers by accident and feel compelled to fight crime. If a character wants to get superpowers, either he'll end up a freak thanks to the accident, or he's a gloryhog who cares more about his ego than with fighting crime and ends up performing Engineered Heroics.
Is that a trope?