This is something that I have noticed since using the iPhone X, but that I have always thought it would be a problem related to testing the iOS Beta. But the information that is appearing now seems to confirm that it is not a bug of the beta but something intentionally done like that by Apple: You cannot use the facial recognition system to authorize your children's purchases.
The family system allows your minor children to have their own iCloud account and to make purchases in the App Store as long as an adult authorizes them from their device. The minor buys an application, the adult receives a message and authorizes or not their purchase. To do so, at least for now, it is mandatory to enter your Apple password, the old-fashioned way.
Apple did not want to confirm anything in this regard, but user complaints are on the rise. It's really awkward having to type in your iCloud password every time you want to authorize a download from your kids. With Touch ID you don't need to, as it uses the fingerprint identification system itself to allow the download request to be authorized. But Apple does not seem to want this to be the case with Face ID. The ill-wishers are pointing out the possibility that your child looks so much like you that he can authorize the purchase without your consent thanks to facial recognition.
But personally I find it hard to believe such a claim: Can you pay hundreds of euros with a credit card using Face ID but not authorize an application purchase? It would not make the slightest sense, and rather everything seems to indicate that Apple has not implemented Face ID for this type of operation. Hopefully now that this issue is gaining more relevance Apple realizes it and fixes this annoying bug.