400V is only used for stoves or instant water heaters, but e.g. our stove uses 11kW actually.

If you don’t have these amounts of energy available, the temperature your instant water heater can reach or the speed with which you can cook obviously suffers (which I suspect is one of the reasons why americans prefer gas stoves so much).

the 3phase is used for motors - a lot more efficient (and the better power factor) than the single phase ones.

For industrial applications definitely, but at home there's few people who power motors with triphase or five phase power.

these are 3-phase stoves, they require a certified electrician to install, because they don't have plugs and there's no wall socket - just a place into which you can easily connect cables.

That makes sense. In the UK you can buy induction hobs that plug into sockets, but they are limited to a measly 3.7kW or there abouts. A nicer 32A induction hob needs hardwired (single phase).

You can have upgrade your domestic supply to three phrase, but AFAICT it's uncommon. Perhaps with electric cars and induction hobs replacing natural gas and petrol, it will become more common.