Earlier quoted context omitted.
" 4kW seems to be the maximum potential drain from the battery. That wouldn't power an oven… let alone anything else at the same time." 4kW is enough to power an entire home continuously, without thinking about energy use, even a large one with a home office with several people working in it + washing machine + oven + electrical stove at the same time . I have the data to prove it, too - 10 second interval power cons…
My air conditioner is 12 kW. No chance.
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.