Being anonymous is actually pretty expensive. The loyalty program is a price discrimination mechanism: going through the trouble of clicking through coupons, discovering deals, signals that you have a higher price sensitivity. The default of taking no action signals a higher willingness to pay. Also, by paying cash, you're subsidizing the card users, some of whom get a bit of that back.
i am paying for my privacy. or, i am refusing to sell out my privacy for any amount of money. and i disagree that it is expensive. the difference can't be more than 10-20%. that's worth it for me.