1. Use their app to scan the bar code
2. Pay with a card
3. A self-service printer prints a receipt/confirmation of purchase.
4. Show it to an employee on your way out the door.
Might be an inventory nightmare, but it could be done.
Sure, the cellphone eliminates the slowdown, but it also eliminates the primary way they currently prevent theft.
Amazon is working on a store that works a lot like you said, with your cellphone, but doesn't rely on the customer doing anything other than logging in. After that, tons of cameras take care of the rest.
Potential pitfalls include the cost of the RFIDs, the ability to detach the RFIDs at any point, the ability to read the RFID on your phone, and alternative entrance / exits of merchandise (e.g. toss through a window).
Are there other reasons that this could not work?
If you used your phone, then it would easy to shoplift. Buy 7 items, but "forget" to scan the last two. Self-service kiosks at least prevents this with weight sensors, cameras, and a human kiosk manager.