Why are there so little young champions?

Because this isn't a JRPG.

I can see two reasons: Originally they were part of the League of Legends which is a Colosseum-style combat arena. You don't put kids in harm's way like that - it's just irresponsible.

Secondly, one of the mainstays of League is pandering to the sexual desires of its large teenage male audience. Hence Miss Fortune, Caitlyn, Sivir being as exposed and "ideal" feminine-formed as they are. Adding child champs means adding both male and female child champs and every champ gets sexualized in some form or another. It would not look good if League was ever compared with child pornography. I doubt you would have to go far on today's interwebs to find explicit images of Annie, despite her age (FIVE YEARS OLD).

So there's two reasons, take em or leave em.

I feel like Annie and Nunu take up the "little girl" and "little boy" themes pretty well. It would be hard to design another child champion without stepping in to their design space, I guess.

Although as for teenagers I'm not sure. Probably because this isn't a jRPG. ;]

Because in Runeterra, people generally try not to be horrible parents. :D

Anyway, people - and I admit that incldues me - generally want cool characters. Cool can be a vast number of things, either by looking cool, of feeling cool. To me, Gnar is cool because he's such a badass despite being so young. He doesn't give a flying fart about those trying to hurt him, and he doesn't even know yet that he is the Hulk. He just doesn't give a crap!

Annie is cool because she does know how young she is, and how powerful she is despite her age. Also, she's cool because she's unsettlingly insane. Probably burned her parents to a crisp because they told her she had curfew.

I don't mind champions below the age of 18. Heck, give me a demonic toddler in a stroller. Just make him cool. :)