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.