>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.