That isn't actually true. It would be perfectly possible to build a payment system where the participants by default don't know the identity of most other parti

That isn't actually true. It would be perfectly possible to build a payment system where the participants by default don't know the identity of most other parties. Like, it would be perfectly possible for a merchant to encrypt the transaction description with a public key of the customer, and their bank only submitting the encrypted record with the amount and the account to debit to the card issuer, who would debit the account and pass on the encrypted record to their customer. That's just a random idea, but the point is that you could achieve much the same result with a lot less data collection if you actually cared to.