How do you prove that it's the kids parent thats giving this permission and not a random adult the kid asked to pretend being his parent?
> Why is that parents can't give consent to their young (<13y/o) child using Google account?
Because the parents probably have to provide written proof and it costs Google money to process such non-automated requests. You basically have millions of children below the age of 13. If everybody wanted to sign up their kids, Google would have to hire people to do nothing else than to just process the written or faxed permissions. Its way easier and cheaper to just exclude pre-13s from the service.