Nowadays, not so much. In the previous decades before password managers, card vaulting, apple pay and so on: yes, if you were typing it in or writing it on forms frequently, it wasn't uncommon to just memorize it.

My point though was that there is a limit to our ability to remember long and random alphanumeric strings, and I find credit card numbers to be that limit. UUIDs are longer and have a much bigger character set.