It's probably because when you go through teen years, you're still finding yourself. So there are a lot of "stereotypes" that can form (like jock, emo kid, etc.) because people are still finding themselves. Being a teen also means you're in between being an adult and a kid; you're accepting more responsibilities as an adult, but you still want to have fun as a child. Additionally, when you're a teen, you're on a roller-coaster ride of emotions, which can create conflict and drama in high school.
So yeah, with those mentioned above, teens pretty much make the perfect heroes for an anime, since the hormones start kicking in and their characters slowly get developed and stuff.