How would that work? The barcode on the item doesn't get rewritten, the checkout counter can't distinguish who picked up which exact item. Even if they did assign unique barcodes to each item, what happens if you take the item off the shelf, and put it in someone else's cart? They'd be charged the wrong price for the item.
The store could make it mandatory to swipe your fidelity care before calculating your prices. They already do something similar with specialized promotions.