Based on: https://support.apple.com/108774 and https://support.apple.com/HT201359
1. If anybody in the family buys or subscribes to something, Apple first attempts to charge the item to that individual's Apple Account (Apple ID) balance, if any.
2. If a family member does not have enough personal Apple Account balance, any excess will be charged to the Family Organizer's primary payment method (usually a card of some kind). The Organizer's personal balance will not be used for purchases made by other family members. If Apple cannot bill the primary payment method, the Organizer will need to make another payment method the primary method. With Family Sharing the Organizer always has to have at least one functioning payment method.
Only if purchase sharing is disabled for the family can a non-organizer have a card of some kind as payment for their account.
Also note: "Some purchases, including gifts, can't be billed to Apple ID balance and will be charged to the family organizer's payment method." "Some subscriptions might not be charged to Apple ID balance."
Ref:
- Family purchases and payments - https://support.apple.com/108774
- How apps, content, and subscriptions from Apple are billed - https://support.apple.com/HT201359
- Check your Apple ID balance - https://support.apple.com/HT202359
- Add a payment method to your Apple ID - https://support.apple.com/HT201266
Adding funds to your Apple ID balance:
- https://support.apple.com/HT201209
- https://support.apple.com/HT208687
Apple does not explain their reasoning for the payment system but I can see it as being a great way to prevent misuse in sharing things with people who are not at a 'family' level of trust and or under the Organizer’s control.