Why?
Today, most children already want to have an email account (or other messaging systems) before the providers allow them to (before they turn 13.) A method that allows them to start doing so at younger ages and also teaches them best practices might help.
How?
The current system could be augmented with an option for younger kids, where every message first goes through their parent or guardian. At a younger age, the filtering by a parent would probably be less of a problem than when they are teenagers, especially if the service provider mandates it for younger ages. The parent could then see how the child is using the messaging system, block a message if it’s a problematic one, or let it be delivered if it’s ok. Then talk to the child to explain what was wrong with it, so they can learn how to use the system well and what to beware of.