I've been expecting Tesco (UK) to do this for ages. They have supermarkets literally operating on this sort of device, you scan+bag as you go, and they have a decent national delivery service.
I wonder if they tried it and found there are less opportunities to upsell so it doesn't pay off: If I'm only scanning products I have then where's the discovery and upsell?
One discovery method could be the "free upgrade". You feel good that they upgraded you to "premium" granola and when you run out, it's an easy upsell since you can just scan the box.
They might even be able to get away with just giving you free stuff outright as a discovery method too, given the huge amounts of consumer behaviour data they must have — as long as their algorithms can predict you have a profitable% chance of reordering the item.