There are RFID based shopping experiences, but I think it's too easy to hack. An RF-shielded shopping bag makes theft too easy. I'm also not sure how accurate the readers are when tags are all piled together.
If you're just worried about customer's bags, it's pretty easy to say customers have to shop with the store carts and can't use their bags until after they've checked out. You could also weigh the bag to make sure the expected weight of the successfully scanned products is in the same ballpark.
The collision problem is discussed by other commenters.
