Right, those won't go away. These offers will likely be in addition to those and because they're more targeted they will be higher value. CVS already has specific offers that you can only get in their app with your specific membership, Target uses their Circle membership to accomplish it.
The medium to deliver this customer experience are out there right now, but they're all working on adding signals to inform which offers you get.
The same way coupons work in drug stores already; there's a stated price and then there's the price with SuperSaver™ membership, which you have to pull out of their app and could be subject to any number of personalizations, real-time or not.
[1] https://getpocket.com/en/