[Toymeister]

I was an early adopter of, Sense, the whole house energy monitor. Yes this system can help you identify problems and trends in your appliances, although I have not specifically read about refrigerator other than one case where fridge energy consumption was compared one year after the coils were vacuumed. In that case he cleaned the coils and consumption dropped.
Sense can help identify HVAC compressor problems (a failing capacitor before it fails, so they claim).

I used sense in my rental, my thoughts were I could prevent problems. That need didn't arise but I could tell if the tenants had extra people in the home.

I discovered that I had a small leak in the AC ductwork in my attic.

I could tell with absolute certainty what certain appliances cost to operate. Much of the energy 'advice' that you get on this forum is rubbish. I have saved a great deal by not purchasing energy saving products, the claimed cost savings are impossible.

Kill-a-watt devices do not compare. That is similar to saying the discovery of fire is similar to Global Positioning System (GPS) technology.