As things stand, we can fly children, but we can't train them as they can't be members. My own children fly with me - and occasional friends. So it's OK for occasional experience but doesn't replace glider training.
Not sure who 'we' above refers to. At BGA clubs (or at least at mine) we have junior members training before their 14th birthday so they can go solo at age 14; that would cover ATC Cadet age range. Agreed, with their parent/guardian's permission, but mine had to sign an OK to do anything the ATC thought I should be allowed to, so I was airborne in an Anson aged 13, and flew a Cadet Mk 3 solo aged 16. If an individual club's rules don't allow it, change the rules.