In a world where vigilante superheroes are the rule, the only question is whether adult heroes would allow it, or the children survive if they went it alone. But in a world where it's more regularized, and not dystopian. . . .
There's always the question of self-defense. Even if you are a child, if trouble comes looking for you, you may need to defend yourself. Especially since your powers may make you eminently exploitable. And training, even if in theory to keep you from being accidentally destructive with your powers) may take you to interesting locales, with plentiful adventures even if they don't involving fighting supervillains.
And in a world where people are less hypervigilant about the danger to teenagers -- that is, virtually every other society that's existed -- or should I scratch the virtually? -- the teens might easily happen into situations where the trouble breaks out. Seeking it out might get them in trouble, but happening on it might let them help.
And if they are weirdness magnets, like so many superheroes, they get the first defense of using their powers: it's self-defense.
(Hmm. If a super has to spend a lot of time training just to keep his powers from being dangerous, he may have no choice except to go into a profession where they will be useful. There would be no time to master a mundane profession well, enough, too. It would also be preparation, because a disproportionate number would go into fighting.)