RFID probably works better if you control the packaging, for instance, for deli counter products. But for packaging that you don't control, you either have to slap an RFID tag on when the items get to the store, negotiate with suppliers to start to include RFID tags in their packaging for items shipped to your store, or arbitrarily limit yourself in terms of which products your store may sell. Not to mention that, if your store slaps on RFID tags itself, it raises the OpEx of running the store as well as needing to come up with tamper-resistant tags, because somebody would be able to steal a product by discreetly removing a tag and then walking out of the store.
In essence, RFID tag technology already exists, and there's a reason why it hasn't taken off in grocery stores.
And if they know who you are because of your phone, and they are doing inventory on a really regular basis (every 6 hours, maybe even less), they might actually be able to track down who it was.
In essence, RFID tag technology already exists, and there's a reason why it hasn't taken off in grocery stores.