You're right, it's partially linkable, but only partially. If I take out cash from the bank and buy something in a shop, it'll get mixed in with all the cash from everybody else buying things there (which obscures the exact purchase) and for smaller denominations there's a nonzero chance that they might get given out again in change before being banked (which makes it hard to prove
any purchase). Until tills start scanning and reporting banknote numbers there's still far more anonymity than you get with digital.
Savings cards I wouldn't touch with a bargepole; I don't imagine anyone who gives two hoots about privacy would.