Aside from the obvious "the audience we're targeting will attach more to a 15 year old detective or 13 year old world saving hero"

Things like school settings mean an easy way to introduce as many characters you want to come up with, and at the same time, force them to socialize, so that's an infinite pool of plotlines to throw in, for starters. For another, this age range also means you're dealing with a population that is likely to stir up drama because they don't have the tools to handle various issues, they're more vulnerable to new emotions - this one is still valid outside of the school setting for fantasy or mystery settings. In your late 20s and your 30s, you're expected to be more set in your ways, not learn new things, be less of a social disaster, and also not have any way to meet new people outside of the company you work at (which is why that's the other popular slice of life setting). Don't worry about how adults can still be plenty of a mess either way, but the target audience doesn't care about that either.