I think the reason for this being the age of most Shonen main characters is a bit more pragmatic than that - it is simply around the age of the target audience.

P.S. No, I am not insinuating that shonen is strictly for middle schoolers, and that no one else could enjoy it. It is just the target audience for the genre, in general, is middle school boys. Like, even the name shonen itself translates literally to "boys' comics", and is officially listed as an editorial category targeting adolescent boys.