There are gobs of fascinating battery ideas like this! Pumping water uphill, heating up enormous piles of insulated carbon, spinning monstrous flywheels, etc. Their plausibility is highly dependent on the environment. So I hope that we'll eventually have a constellation of these wild batteries supplying the world's storage needs. I suspect that we'll see the idea you described gain more adoption. The result: fleets of "air battery" homes climate controlled by municipalities via opt-in smart thermostats (and credit incentives) to ease grid loads.