Wouldn't the bank still know your full purchase history (since they know what numbers are tied to you)? So they'd in fact get a leg up on the competition, who get a more distorted view?
Unless they work with an analytics system that mastercard, visa & amex participate in to link card numbers to invoices for better advertising & affiliate data.
I know FB & Google purchase something like that from one or two credit card companies, so I wouldn't be surprised if merchants were in to it too.