Specific institutions, like finance, need to be able to discern your identity in some way in order to remain viable economic institutions. Provenance of monies can be a big question, and an important one, when dealing with people who spend their time in financial crime. If financial institutions could use a technology that is similar to PGP that maintains an identity without needing to reveal who you are, to me this is privacy. There's obvious exceptions to that, but generally I think it's a good idea given that one of the major ways merchandisers collect data on you is via transactions.
This has also a positive side. E.g. I never shop shoes online. So my bank called me one fine afternoon because someone used my card number to buy shoes. That store only sells women's shoes (I am a man). This was not consistent with my "profile" (of course I have one) and they cancelled the transactions, refunded the money, notified VISA and merchant, and called me to tell me that they will see the transactions on my logs (-50, -100, -150 and then +50, +100, +150).
I expect and demand that from my bank, but not from Facebook: "hey why aren't you in your typical pizza resto and you went across the street?"
this phrase is an oxymoron. Banks need to monitor, track, report activities. Central banks 'siphon' all transactions every day/week/month, so they can cross reference that Henry Bemis made in total $100m transactions today even if he used 50 different banks. A single bank can only track/monitor for AML its own clients. Central Banks can do that. Tax authorities can tap into bank's data.
Side note: There is no such thing as privacy when you use a card. The only thing that 'protects' you is that your bank won't sell your data to Facebook. But NatWest banking app DOES talk to FB when you fire it up... so... at least they don't tell FB (yet) everything you do.