It’s not hard at all to get a new credit card. Report it lost and get a new one. In the US I’ve never seen a bank charge for it, and several times have simply gotten a new one sent to me unprompted because the bank had been informed the card was compromised. Sure it’s not the same as creating a new gmail account, but it’s still incredibly easy.
Also, banning credit card numbers is going to be problematic... most smaller operations are not (and should not) be handling their own payment processing and should never have access to card info. Even if you do and you hash it to match against that’s iffy from a security perspective and would likely run afoul of any decent PCI auditor.