This is perhaps an Italian problem? In the UK loyalty cards are generally free, even if you were required to have one for the scan-as-you-shop systems. This used to be only Waitrose before the other supermarkets (Sainsburys, Tesco, etc) adopted them.

Same goes for Switzerland. Both Migros and Coop offer this, and both require a loyalty card (and also a payment method, obviously), but those are free too.