1kW isn't driving you anywhere though(even if we ignore all the dangers of having a nuclear reactor in a car). A typical automotive engine produces 100-300kW.
Hmmmm a normal boiler for a 4-person family home is about 8-10kW so again, probably not. At least not for heating. But for normal power consumption should be ok, especially if paired with some storage device to account of periods of higher consumption(running a 3kW kettle for couple minutes for example).
Well yeah not the average household obviously but if you really wanted to get rid of your dependency on the grid it would be somewhat possible. As opposed to say drive a at least 70 HP ~ 50 KW car. Not a proposal for everybody of course but for lets say political idealists.
As far as the 3kW kettle is concerned having a battery to provide for these surges is entirely viable.