We either de-carbonize energy in which case air-conditioning doesn't contribute to CO2, or else we fail.
There is no world where we convince the vast majority people to forgo air-conditioning. Billions of people in India, China, and Africa want air-conditioning.
Energy austerity is not going to save us.
Although I do agree with you in principle. One of the lasting impressions I got from the early Covid lockdowns was that even though we stopped a good chunk of the world from driving to work, flying, running factories, etc., we didn't come close to reducing our energy use enough to prevent more warming. Those lockdowns were a huge exercise in "energy austerity", and they weren't enough.