What you get in the US is single phase 240VAC that is split into two 120VAC circuits. There are actually use cases for three phase AC in a home. My house has three phase (I'm in Germany.) I have one outlet for three phase. It was used during construction to power equipment (cement mixer, hoists, stucco pump, etc.) I occasionally use it to power an arc welder.

It would be difficult to predict how things were if they were different. Who knows what voltage, frequency and phase would be in use. In any case the appliances would be compatible, and stoves/ovens already have multiple options to wire them in 1, 2 or 3 phase operation. And yes people do have 3 phase motors in their households. 3 phase electricity allows to deliver more power for same amount of copper.

@JRE Does that equipment actually need 3 phases or does it just utilize the higher voltage between phases? I know that in industrial settings 3-phase motors that actually need all phases are used. However, it's not clear to me that hoists etc. would need the same thing.

@Justme How does 3-phase electricity allow more power for the same amount of copper in a residential setting (i.e. not in high-voltage lines etc.)? If you have only 2 wires with an opposite phase instead of 3 then you can have thicker wires for the same amount of copper.

The equipment used in building the house actually ran on three phase. The welder does, too.

@QuantumWiz But it would make no sense. If you already need 3 phase mains, why go through the trouble of connecting an exotic 400VAC single phase motor to it, with all the electronics involved such as starting caps while you could just use 3 phase to begin with?

@QuantumWiz You have protective earth too. 230 V 16 A single phase = three wires needed and 3.6 kW output. 230/400 V 16 A three phase = five wires needed and 11 kW output. 83 % more utilization of the copper. Three phase motors are much easier to start too, with no need for run nor start capacitors.

It will be nice to have the highest power access possible as EV charging stations become part of most houses. Pushing electrons into your car with a bit more potential will speed your charging and I'd think that faster charging speed will be worth the modest extra cost for 3-phase if 3-phase is available in your neighborhood.

@Justme You said: "If you already need 3 phase mains". But you don't need 3-phase mains coming to your house as proven by the arrangement in the US. You can have a step-down transformer such that you get only 2 phases and a neutral from a center tap. You said: "an exotic 400VAC single phase motor". But single phase motors aren't exotic as proven by the US. Maybe that particular voltage for it would be exotic for it but that is an artifact of history.

@winny I would think the protective earth and neutral wires wouldn't have to be any thicker just because you have only 2 (thicker) live wires?

@QuantumWiz Your comment proves my point. If 2 phase power is what you have then appliances available need to be compatible with it. If you have 3 phase power available then appliances available need to be compatible with it and it allows 3 phase appliances which may be simpler.

No, that’s the beauty of symmetrical three phase, same 2.5 mm^2 for all conductors in both examples.

You're assuming the MV distribution infra is all three phase -- in much of NA, it isn't, and even when it is, 3phase MV in older non-industrial areas is set up for an open high leg delta secondary, not a symmetrical wye, which throws everything for a loop

It would be very convenient for those appliances which use induction motors. Three phase induction motors are a bit simpler than single-phase. Apart from that I am not sure if it is a big deal.

@marcelm My impression is that in e.g. stoves each hot plate only uses 1 or 2 phases, not all 3.

In the UK, 3-phase to homes isn't common, everything runs of 230V and works pretty well. So in your domestic stove example, all the hotplates are connected to the same phase, because most customers will only use one. Commercial kitchens usually use gas, so there wouldn't really be a market for 3-phase stoves. And there aren't many big motors in homes

I think the only things that use three-phase (as opposed to just needing lots of power) are AC motors, and these are tending to be replaced by inverter drives anywhere you need variable speed (or something like a thermostat) - heat pumps and so on.