What actually wins this fight is on the other side. A two-connector polarized NEMA 1-15 plug is a tiny, convenient, easy to use form factor that will still deliver 1400W. The experience of a normal consumer plugging in their normal junk in the US is just plain superior to the poor folks across the oceans charging their devices with BS1363 connectors that are almost bigger than the phones. And don't even get me started on Europlug.
Spend $5 or more an outlet and the plugs will work quite well.
(These kinds of things are what you should focus on if you build - materials are relatively small compared to labor and doubling your material cost on things like outlets can make a much nicer house. And if you want a UK outlet, you could get one wired up.)
Plus, I will fight anyone who suggests that 1400W is enough for a decent kettle ;-)
[0] Admittedly this was mostly included to offset the idiosyncrasies of final ring circuit wiring, but it's still better than just a big breaker.
I think your pretty spot on that most people do not need 3 phase, even in the limited cases you mentioned. =)
I can think of three, sort of:
1. A well pump, pumping from a high-producing well, into a tank or pond at the surface, where the pump is sized to efficiently pump somewhat less than the well’s production.
2. A pool or pond pump which, by some miracle, has been correctly sized for the system, and which, by some other miracle, is more appropriate in the application in question than an Intelliflo VSF or similar pump.
3. HVAC fans. But these are usually pretty small, and better systems usually use ECM motors.