4kW is enough to power an entire home continuously, without thinking about energy use, even a large one with a home office with several people working in it + washing machine + oven + electrical stove at the same time. I have the data to prove it, too - 10 second interval power consumption logs for the last 4 months for my house/office, and I never had a load of more than 3.5kW. To be fair, this is all with modern, top of the line appliances, so yes that 199$ no-brand Chinese oven will probably draw a lot more power, but still.
Worst case, you'd need a second 'peak power' supply, which could provide e.g. 6 or 8 kw for 10 mins max, maybe using some sort of XXL capacitor. I don't know about the EE side of this, or whether such a thing exists already, just saying - 4kW is perfectly feasible and even heavy users would maybe need just a little bit more.
(of course this also assumes you have a better quality house than the standard American cardboard 'house' in which you need A/C running 24/7 just to not die in summer).