I don't use loyalty cards, but I don't pay more because of it. There still exist stores that don't have them, and my observation is that the regular prices on those stores are about the same as the "loyalty card discount" price at other stores.

The "discount" you're getting with a loyalty card is a sham. The regular prices were just bumped up to give the illusion of a discount.

More to the point, though, the issue I see with your analysis is that you're assuming that privacy has a single value. My privacy is worth just as much to me as a wealthy person's privacy is to them. That others value them differently is unimportant. The cost of the loss of that privacy is the same regardless of income, but only the wealthy have a way to minimize that loss without going to extreme measures.