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.