So, I've just read bs0u0155's Super Fast Kettle and Loris' High Speed Kettle and a number of the anno's, and I had a flash. I'll call it Rocket Kettle, as it borrows from the world of rocketry propellants.
In the simplest variant, you would have a reinforced all-metal and/or ceramic kettle into which
the desired amount of cold water will be placed. You'll still need the requisite whistle, though you may wish to direct it's output away from where anyone might stand or any flammable items. A nozzle is directed into the water below the waterline at just the right angle so as to avoid excess venting of scalding water, while encouraging full mixing of the water. Said nozzle would be connected to a pipe, leading to a small chamber with a small silver or platinum-plated catalyst screen inside just downstream from a valve. Above the valve would be a strong, sealed, refillable container with the correct amount of High Test Hydrogen Peroxide (HTP). When you want hot water, open the valve. The HTP, either under gravity influence or an external pressure source (though the gravity variant will likely self-pressurize rather quickly, hence the strong, sealed container), runs down to the catalyst screen, where it commences the rapid and highly exothermic breakdown of the HTP into 600C steam and oxygen, which then is directed by the nozzle into the cold water, vigorously mixing, frothing/oxygenating and heating the water. Very rapidly. Rocketlike, in fact.
As an added bonus, the extra oxygen liberated will improve the air in the room, and I don't know what bonus effects will entail from oxygenated water for your tea.
Getting the correct water/HTP ratio to end up with the right amount of hot, oxygenated water for your cuppa will take a bit of math, which I don't feel up to at the moment. Should be right fast, though.
Variations on the theme could borrow from bs0u0155's Super Fast Kettle in having a continuous draw from the small outlet we have in the US and using the power to run a still that takes drugstore (3%-5%) hydrogen peroxide and distills it into the HTP range (68%+), thus making it refill itself from a commonly available OTC product, rather than having to order from the rocket supply house.
I've other variants, but they don't really belong in the kettle category...