If you don't think this crime is a big deal, then why do you think this crime would matter if it was in the public record tied to their name? These two ideas you have are not compatible.

I don't think stealing a pack of gum at 14 years old is a big deal, but many people have a huge problem understanding proportionality: To them, it's binary. You're either a criminal or not a criminal, and if this kid's record shows "shoplifter" until he dies, a significant number of people, including employers, will lump him into the "criminal" bucket for the rest of his life.