What about a kettle with a giant battery pack that charges when idle and boils at 10kW when you press the button.
At that point one might as well get an instant boiling water tap system.
Photonicinduction's 10-second kettle[1] doesn't use a battery, instead it uses his 100A 240V input through a big variac to run at 10kW (440V, 22.7A). This isn't good for the longevity of the kettle he used, sadly.