I assumed that they'd just link it up with credit cards even if I refuse to give my phone number. Or, maybe they'll invent some common encrypted face fingerprint with which they can identify customers across companies.
Most of the small indi-shop ipad POS devices do this already. If I swipe my card at one, I get an email automatically with my reciept. At some point in the last few years I must have put my email address in one and obviously it's shared.
Credit cards are harder, because people switch those. I have had the same phone number for over a decade. This way, they keep historical data in the same profile.