The failure mode of fridges is generally much simpler. Most over temp conditions are due either to power loss (in which case your temperature monitoring and/or internet is out), catastrophic failure (in which case it's pretty obvious) or someone leaving the door open. For the last 20 years or so, fridges have had audible alarms when the door is open for more than a minute or two -- which pretty much solves the problem for a COG of about $10.
On the other hand, I really would like a bar code scanner on the fridge so when I use up an item, I can just scan it and have it added to my grocery list/order. (I guess I could use a phone for this instead.)
I struggle with what my fridge really has to say to me. Perhaps there are a few appliances that are smart and have interesting things to say, but the fridge isn't high on the list. Alarm systems, maybe, but for alarms 24x7 reliability is critical and the IOT folks haven't been particularly successful at demonstrating this. Maybe a thermostat, but except for vacation houses it's hard to see the benefit of being able to remotely control/monitor temperature.