Much smaller batteries can do more a 3S lipo battery with 50C discharge rate that weighs probably around 100g can output about a kilowatt discharge without break a sweat.
I am not doubting the instantaneous output in power. Batteries have always been great at that. I am doubting the energy storage capacity and ability to output that power over time (energy). Humans are a lot heavier than flying quadcopters and quad and multi-copters almost universally don't last for more than ~30 minutes. High power but not much actual energy storage compared to chemical.
This is what allows drones to be a thing.
The large DJI drones like the T40 are 4KW per rotor… https://www.dji.com/uk/mobile/t40/specs