Keeping track and sticking buttons all over the place is going to be an "early adopter" feature. Once we get to an overwhelming number of "buttons" it will make sense just to put up a couple cameras similar to the Microsoft Kinect and use hot zone + gestures to do the same thing. RFID in boxed products might help out but the buttons will end up being a mess right quick.
It is cheaper to put microphone and ask for food, similar to regular shop: "Hey, Amazon", "Order, please", "Bottle of milk and bread", "Bottle of milk «Foo» $2,50. Bread «Bar» $1,75. Total: $4,25. Confirm?", "Yes", "Order accepted, wait for delivery.". Something like Siri, but activated by push of hardware button on the fridge.
Yep. But it's a closed-source always-on cloud-connected microphone that lives in the middle of your house, which creeps the hell out of a lot of people (including myself and most of my housemates).
Interestingly enough, when I signed up for Amazon Fresh, I got a version of the Dash that is multipurpose. Instead of having buttons everywhere, mine has a barcode scanner, and voice recognition. When I am out of eggs, I just pick it up, push the "Mic" button, say "Eggs," and it appears on my "Dash" list when I log in to Amazon Fresh.