Your central HVAC system, heating, can run on a very small generator though, since the heat is provided by burning propane/NG/fuel oil.

AC needs electricity for the cooling itself too - lots and lots.

As others have noted, yes air conditioning an entire house takes a lot of power, but if we're talking about large scale disaster scenarios you don't need to air condition an entire house.

My car can power a windowshaker and a refrigerator for days between charges. It can air condition itself for about a week. If things are at a place where that's not enough why would I stay there?

Unless you have electric heat.