This to me is part of a general trend wherein only those with the awareness and resources required will have privacy. For example, if you do have the funds, send a private shopper. But an even more direct example is skipping the discounts associated with club cards for privacy reasons. This will further entrench the class divide between the wealthy and the rest of us.
This may actually close the class divide a little. The thing with privacy is the more wealthy you are, the more valuable it is. For example, if I want to sell something, I will want to target the wealthiest first. Same thing for scammers, and newspapers will follow celebrities. Who care about the poor, there is no money to extract from them. So let's get back to the private shopper. A rich and famous man will want to…
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.