If you can transmit that amount of heat that quickly, I think it'd be much more convenient and feasible to have it in the form factor of an instant-boiling-water spout next to the sink, rather than a kettle. Then, rather than having to fill the kettle first, you directly get the amount of hot water you need into the vessel you want it in, and you can put a precise amount of heat into a precise amount of water flowing through a pipe to emit it at the right temperature.
By the way, you can already have a boiling water tap today, you just buy a device that uses hot water tank to store the energy you rather than the battery. Insinkerator sells these. It might not be as energy efficient as the hypothetical tankless water boiler as described by you, because you have some losses from the heat slowly leaking away from the tank, but given the battery costs, I suspect that over the lifetime of the device, these losses add up to less than what battery costs.
