For made at home items and non-tagged items, they could also make RFID stickies, where you scan them when you put the item in the fridge, give it a name or take a snapshot with the built-in camera, set your own expiration date, and it tracks how long it's been in there.
If you focused enough on usability, you could make the whole thing feel streamlined and natural. The fridge itself could dispense the RFID tags, and you could just reuse them by reloading it with the old ones, for example.