You're assuming those jobs exist. It's not whether they could do something better than a "normal" human, but also that they'd be welcome as an employee.
If you've got lots of superheroes, there's a much bigger question of how the society as a whole handles a large, powerful minority. (Which is precisely why superhero comics have been such a neat analogy for colour, gender and sexuality over the years.) In the comics they're a very small minority. When you get enough of them to be a game-changer, the government are going to be thinking very seriously about it.
Charles Stross's The Annihilation Score has this scenario, where a significant number of ordinary people spontaneously develop superpowers. He has a two-pronged approach to this. The first is that when people realise they have superpowers, some of them do go out and try to emulate Batman, so there's a conscious effort to form a police-led superhero squad which can go out and arrest criminals with superpowers, following the normal rule of law. The basic concept is that superpowered people must not be above the law. This is good enough for a lot of people - it's why people do become police officers, after all.
The second prong though is a nastier feature of Stross's Lovecraftian plot arc - the reason people are getting superpowers is that the barriers between universes are becoming weaker, and people using superpowers are a big flashing "feed here" sign for various entities. Its's not (yet) a case of the Elder Gods coming to visit, but microscopically small nasties pop up inside the superhero's head and eat small chunks of their brain. Without protection (provided by the government agency who knows about this stuff), your average superhero has a few months before CJD-ish symptoms set in, leading to a fatal stroke not long after that, with a brain that looks like 3D lacework at autopsy. Stross has basically set up a scenario where only government-sponsored superheroes are going to live long enough to prosper.