It would be really cool if it generated new numbers each time and had an amount coded to that number. So when I wave my Apple Pay device over the reader it would display the amount on the device, I would approve, and then a number would be handed back that's only good for that amount.
So, not only can a single merchant track you, but all merchants can cross-reference the data they have about you and track your whereabouts, purchasing habits etc. They just don't know who you are anymore, because that information is not transmitted. Unless one merchant asks for your email or home address, and this merchant then adds that email to a shared database, at which point we're back to step 1 and the merchants know everything about you.