> I know the US already has a different 240V plug shape, so it might have to be an unlicensed installation, but surely someone wanted hot tea faster and did that calculus before?

How expensive would a proper AC->DC->AC brick for that power level be?

Not so simple, you'd have to use a 'drier' or 'welder' socket for that otherwise you won't have enough power. A single circuit in Europe is 240V 16A or 3840W!

A pure sinewave inverter for that kind of power is maybe 600 to 1000 bucks or so, then you'd still need the other side and maybe a smallish battery in the middle t stabilize the whole thing. Or you could use one of those single phase inverters they use for motors.