But you're probably not, and that was my whole point - my stove top is rated at 10kW, too, yet even when using alongside all other appliances in my house I have never gone above 4kW actual use. Actual need != summing all the nominal maximum rated loads of all appliances. In other words, it's not because your AC is rated 12kW, that you'd need 3 of these battery packs just for the AC. You might need 2, or maybe 3, I'm not saying that 2 (or 4) kW is enough always, everywhere for everybody - but there is no 'normal' (middle to upper middle class) home anywhere that would need 5 or 10 of these units, as is suggested at various places in this thread.

(Probably some jackass is going to downvote me because they think this violates conservation of energy, but no — those 12kW coming out of the heat exchanger include the 5kW of electrical energy that went in, plus another 7kW of heat that’s being extracted from the air being conditioned; and if you were to try to run a heat engine off that 7kW of heat difference, you wouldn't be able to recover the original 5kW. All perfectly thermodynamically copacetic.)