Young children can not create a bank account so they can not get money transferred. In case their parents set up a bank account, the parents will have access to that money and see any transactions.
Now you are probably a good person who would not steal money from your children. However some parents are not good people.There are also a lot of cases where parents don't want their children to have things they need, like soap or tampons. Doubt much has changed about that from the time I was a child. It would be a lot harder for children to access things like that if no one can slip them some secret money.
That way nanna would need to know that the children are struggling with this. A lot of children wouldn't tell from the shame and since they are doing something 'forbidden'. I know I wouldn't have told my grandma.