> Why is this necessary if I'm paying Anthropic with a credit card?
You can have a CC / Visa / MasterCard when you are under 18 years old, but you need to be 18 or older for Claude. That would be one reasons why CC does not work.
Or maybe they suspect you opened a second account after your first got banned for whatever reason. Like you said it's easy to get a new card.
Incidentally I checked my local laws and it's not possible in any of the banks (UK) to add the underage person to my CC account due to their ToS and perhaps regulations.
Debit? Sure, some banks will issue them to 11-12 year olds. Credit? Apparently not.