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.
It's not clear you're actually buying any privacy. The cameras they have in stores will be used for tracking customers soon anyway, and not having a tracking identifier associated with your transactions make you stick out like a sore thumb.
camera tracking is illegal in many places, and while my shopping may stick out, it still can't easily be tied to my identity. i only pay with cash too. the only place where i use cards is on ATMs.
the only place i have one is a grocery store where their loyalty program price is listed on the shelf tag and is lower, often by quite a bit (a third to half off is common). even then, i use one of the meme phone numbers (local area code + 867-5309, 678-999-8212, 281-330-8004, etc.).
I say 'no thanks' when the cashier wants to know my phone number, even if I am paying cash.
It is almost impossible to remain anonymous in the consumer space, even if you are really trying.