This isn't a matter of trust. They'll happily pay ME back for anything they buy from APPLE using their own devices. It's just a bit silly and inconvenient, that's all. As mentioned, these are adults who have cards of their own connected to their iTunes accounts. Just as they can connect gift cards to their account and use those independent of the card on file, it seems logical that the same transaction flow would apply to their credit/debit cards as well.
It is a bit odd that Apple recognizes these family members as adults, but requires me to pay for apps, games, movies, etc that are purchased by my siblings and parents who have their own families, live in their own homes, and have their own preferences.
Our main goal was to share Apple Music (since we have the family subscription). It's just weird that Apple assumes I want to pay for all of their purchases just because I've invited them to the Apple Music subscription, or iCloud sharing. More granularity seems needed here.