Not necessarily. The easy way to implement this in-person would be to give customer-specific coupons. You could get an email that says "use your loyalty card at checkout and get $2 off eggs". Then you just give everyone a different discount and only the privacy-minded folks end up paying the (inflated) sticker price.
A significantly more complex hypothetical that I don't think anyone is doing yet: With digital price tags and customer tracking you could show different prices to different customers in-person. For example, when Alice goes to the eggs it could say $2 and when Bob goes to the eggs it could say $4. Then you just need to track the customer to the register to make sure you give them the price that was displayed. I believe the amazon "go" stores were doing the whole customer tracking thing so we already have the necessary tech demonstrated in real stores.
i really doubt the downsides of adding that layer of complexity can compete with the upsides of surveillance pricing.
FYI, I specifically mentioned Aldi because they don't have loyalty cards. I understand that might not have been clear to everyone, so I'll edit my comment to make it clear.
"The easy way to implement this in-person would be to give customer-specific coupons. You could get an email that says "use your loyalty card at checkout and get $2 off eggs"."
This already happens. We've been getting personalized coupons from our local store for 15+ years now.
>Then you just give everyone a different discount and only the privacy-minded folks end up paying the (inflated) sticker price.
This is already happening at Lidl. I was standing in line one day and the lady in front of me asked if I had the app, because there was something like a $5 off $50 purchase coupon in there I could use. I did have the app and checked, but my coupon instead was for $15 off $150.
Thinking a little more deeply about it, every time I go there I tend to spend an average of around $125. My hypothesis is that they have that data and know a customer's average spend, so they tailor the coupon's dollar amounts to the customer to entice them to spend slightly more than they usually do.