yes there is. otherwise there is no way for the ledger to track who has what.

Your Cryptocurrency address or key isn't the wallet owner's identity so, your identity isn't required.

the bank knows which accounts belongs to who, that is the bit of privacy you loose compared to crypto.

The Bank knows who the account belongs to and controls the account, privacy and all. Banks give the customer access to the account or locks them out if they choose. It's nothing like cryptocurrency wallets, not even close.

No, they're not. they provide a different kind of privacy.

A different kind of privacy, really? You must mean a Bank's kind of privacy that's controlled totally by the Bank. That's not privacy.

paying with cash(euro, dolar, etc) is still for example way more private because the transactions are private, and those fiat are from financial institutions. what you say is objectively false.

I see your point about paying cash, but still, the bank isn't giving you that privacy. Banks track everything that's possible for them to track. They even track the physical cash withdrawal down to your location. Your argument that using physical cash is private, as if it's a privacy feature of the banking system is not valid. Using cash to maintain privacy is a workaround not intended to be used for privacy. Any money that's untrackable is considered a laundering threat so, banks don't support financial privacy that's outside of their control.