I don't know if Apple Care One is one of the subscriptions they mention below, but if you review how Apple takes payment for things if it could use your balance it would. I am therefore guessing Apple Care One is one of the subscriptions that can't be paid that way.
How apps, content, and subscriptions from Apple are billed - Apple Support
Apple Gift Card and Apple Account balance can't be used for some purchases
• You can't use your Apple Account balance to send gifts or gift cards.
• For some recurring charges, like AppleCare+, you can't start your subscription with Apple Account balance. But as long as you keep another valid payment method on file and your Apple Account balance would cover an entire charge, your recurring charge will pull from your Apple Account balance.*
• Some subscriptions might not be charged to your Apple Account balance.
• If you use Family Sharing, your family members can't spend your Apple Account balance. Funds that you add to your Apple Account balance are available only to you. Learn more about how purchases bill to your Apple Account balance.
• Some purchases might require that you have a credit card on file, even if you use your Apple Account balance to make the purchase.