In the entirety of my life, most of which has been in the Chicago area, I have never seen a home with a generator for the fans and thermostat of a home. For that matter, the only home generator I ever saw was one my grandfather bought which he only used once to see if it worked.

They're pretty common where I live (SE Michigan) because the electrical grid is quite a bit less reliable than the gas distribution network. To the point where 5-10% of customers in the service area lose power in any given big storm.

We have an (almost[1]) all electric house. A year ago we lost power for six days. Last spring we had a generator installed. Over the summer we lost grid power for five days but the generator worked flawlessly the entire time.

I don't like having gas for a number of reasons and if the grid was more reliable we would never have bothered, but, for us, it's just so much more reliable.

[1]: We have two HVAC systems that service different sides of our duplex-ish house. One side is a ground source heat pump, the other is a 95% efficient gas furnace.