> If your purchase habits are uniquely trackable, upon switching to cash you'd need to modify your purchasing habits sufficiently to disassociate them from your past-self.
I do not think that's quite right, at least in this instance. For the study in the article, the use of a single credit card number links purchases together, which is what enables the de-anonymization. If you pay with cash, there's no purchase identifier, so it is more difficult (impossible?) to link multiple purchases to an individual (anonymous) person. This potentially changes, if people are tracking serial numbers on bills.