Cryptocurrency is not necessarily anonymous. Buying bitcoin from a broker leaves a record connecting your payment method to your wallet. Even if you mine them yourself, doesn't your IP address show up on the public ledger? I guess if you somehow bought bitcoin in cash...
Is there a more private cryptocurrency I'm not considering?
I consider it more private than like a credit card at least your name's not attached to it.
And if you really want to you can just use a credit card at an on-ramp exchange, then take that and swap it for a different crypto on a exchange that doesn't require any registration. Then it becomes effectively completely anonymous.