So...
- You can just add a member to your "family" of your Apple ID
- Child accounts created this way can make purchases using the payment method of your Apple ID, but every single transaction requires confirmation by you, so you can deny anything you don't want your child to purchase
- Non-child accounts added to your family can make purchases with your shared payment method without your confirmation. I assume Apple does this so you only add people you trust instead of random people you just want to share purchases and subscriptions with
- No matter who initiated a purchase in an Apple family (you, a child or your partner for example), you get an invoice to your email stating exactly what was purchased, by whom it was purchased, when and how much it cost
But no, you apparently created a "regular" Apple ID for your child, added your payment method to it and after THREE MONTHS you noticed that 8k are gone. Then you run to the press and complain that this was even possible and wonder why neither Apple nor your bank marked any transactions as a fraud.
YOU authorized your child to use your payment method freely. There is no fraud (except for you). There were multiple ways to notice what's going on (bank account, invoices from Apple) before your child spent 8k. You should show more interest in what your child is doing, especially on the internet. That's bad patenting.
I hope you don't get any more money back, you deserve every bit of it.