European plugs aren't aware of any hot/neutral polarity and devices are not built to treat a neutral phase differently from a hot phase. A separate grounding wire is used for safety.

I'm assuming most European appliances use double-pole switches?

United States 240V is single phase. 120V is split phase, with the neutral drawn from the middle of the coil.

You're right, I was confusing that with true multi-phase power.

>American 240V outlets are two-phase (two hot plus neutral).

No, that's single-phase. The "phase" is measured across the hot wires; the wire itself isn't the phase. There's no such thing as "two-phase".

Yeah, I got confused because some people lazily refer to split phase as "two phase". Apparently I need a refresher session with my textbooks. :(

Actually there is janky 90 degrees out of phase two phase power. Who knows if there's anywhere still using it but it was a thing.