Q: Family Sharing without agreeing to pay for their purchases?

This may help you:

Family purchases and payments - Apple Support

See the section:

Making purchases

After you set up your family, any time a family member initiates a new purchase it will be billed directly to your account, unless that family member has gift or store credit. First, their store credit will be used to pay the partial or total bill. The remainder will bill to the family organizer's card. As the family organizer, any receipts generated by the transaction will be sent to you. Learn more about how iTunes Store purchases are billed.

So, as I read it, each family member can set-up their own gift or store credit.

As to the content you want (or don't want) to share:

What types of content can I share with Family Sharing? - Apple Support