Superheroes don't get career choices. They're beings with powers which dictate what they'll do. Unlike us, with our grab bag of vague skills and strengths, we're asked to believe that having a super power is so overwhelming that it forces people into one specific career. They must be vigilantes, living outside of society's rules... Really?
Personally I'm not convinced that having an extra sense or strength would be enough to get me off the couch, let alone loitering in dark alleys to fight crime. Realistically, if I had Aquaman's ability to telepathically communicate with sea creatures, or Daredevil's radar, I probably wouldn't be much more motivated to battle evil than I am now. I'm not discounting it completely, I'm just saying that it's highly unlikely. Obviously I'm aware of my responsibility towards my fellow humans; I donate money to various charitable organizations, and donate old clothes and books instead of chucking them out, I recycle and even compost (braving the horrible swarms of flies which populate my fetid composting bin.) Sadly, this doesn't translate to actually physically doing anything dangerous (beyond the aforementioned flies, which don't really count, do they?), and I just can't imagine that having powers would force the issue.
This means that we're being asked to believe that simply because a person has a lot of power, they'll definitely become really responsible, particularly for the health and well-being of people they don't know. If this were true of human nature, wouldn't more people be clamoring to work in the peace corps, be policemen, teachers, or even nurses and doctors? There would definitely be an overabundance of volunteer workers, since most vigilantes don't get paid, they're just doing it out of the goodness of their hearts apparently. Thing is, from what I know about teaching, there really isn't enough money in the world to pay me to do that, let alone risking my life as a policeman, and as we established with the flies, I'm not good with bodily waste, so nursing isn't the way to go either.
Let's suspend disbelief for a moment and assume that this is true: For whatever reason, individuals who get a power feel that they have to become heroes and work outside of the law to do so. Obviously some powers can't be hidden (e.g. being covered in blue fur, being large, green and monosyllabic, or having giant wings) and would force a person to choose an unconventional career. Then there are the heroes who have an emotional need to fight crime on their own terms. Outside those whose powers preclude them from living a "normal" life, there are the heroes like Batman. They fight because of a personal compulsion, and so have even less choice about what they do. He essentially has the hero version of obsessive-compulsive disorder, except instead of washing his hands repeatedly, he feels that he must fight criminals.
What about the idea that these people have secret identities? They have time to engage in a consuming career of illegally fighting crime, and simultaneously sustain an entirely separate career and social life. I don't know about you, but I'm lucky if I have time to fit in keeping to my work deadlines, let alone see friends, go out, buy groceries, and do whatever else it is that I'm supposed to do in order to have a healthy, balanced life. Okay yes, I could get rid of my television, that would probably give me an extra couple of hours ever day, but how much energy would I have for those two extra hours? No, even the people I know who don't have a television would be extremely unlikely to find time for a secret life.
The only similarity between my own career motivations and those of a person who becomes a (fictitious) superhero, is that I have found work that I can do with the natural talents that I have - I write and I design. These are skills that I've had for almost as long as I can remember. I enjoyed them, and I always thought that I'd have a career that encompassed them. Realistically, with these talents came an obvious career choice. It's hard work which I enjoy partly because I'm able to do it. I make time for both writing and designing because when I do both, I'm happier.
The key here is happiness. Ideally, we do work which we feel we can do well, which will make us happy*. In life this isn't always how it works out, and in fact, even the ideal career has it's share of frustrations, so reading stories about people who do the work they love is incredibly appealing. The metaphor of the superhero is particularly apt, since it is, in a sense, a bit of a modern fairytale to wish for, this perfect joy in ones work. Being allowed to watch superheroes find their perfect path to doing the job they were made for, is a pleasure. Superheroes chose correctly, they did it right, and this is the crux of the superhero trope. They are good at something, and whether that's because they have a physical talent for it, or an overwhelming desire/compulsion to do it, they choose the job which they can do best and that is a very satisfying thing to witness.
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* Please note that I said "ideally."