I may be missing something here but why isn't child benefit means tested. And a benefit that you apply for, rather than getting automatically.
When we decided to put tot into daycare, we applied for child tax credits. Filled in many forms. Produced much evidence. Then got nowt as hubby earned slightly too much. But well, that was fair I guess. So surely the same system can be used to figure out who gets child benefit. Making people apply for it rather than receiving it automatically is bound to reduce the amount paid out.