> The center tapped transformer that provides residential split phase 120/240 on its secondary winding connects to just 1 of the 3 grid phases on its primary winding.
I believe that's a USA peculiarity. Where I live, the usual residential and commercial wiring is from 13.8 kV to 127V/220V through a three-phase delta-wye transformer, in which the primary connects between each pair of phases, and the secondary connects between one phase and the neutral (the high-voltage primary side does not have a neutral). When one phase of the high voltage side is lost (very common, since each high-voltage phase is a separate wire and has an independent fuse upstream of the transformer), what happens is that one phase of the low voltage side stays normal (the one between the two intact high voltage phases), and the other two have a lower voltage which varies depending on their relative load.
Look up Wye vs Delta; but the basic point is in delta the phases are connected in series with each other, and in wye they are connected in parallel. It's easier to visualize when you can see the tap points on the transformer secondaries though.
I believe that's a USA peculiarity. Where I live, the usual residential and commercial wiring is from 13.8 kV to 127V/220V through a three-phase delta-wye transformer, in which the primary connects between each pair of phases, and the secondary connects between one phase and the neutral (the high-voltage primary side does not have a neutral). When one phase of the high voltage side is lost (very common, since each high-voltage phase is a separate wire and has an independent fuse upstream of the transformer), what happens is that one phase of the low voltage side stays normal (the one between the two intact high voltage phases), and the other two have a lower voltage which varies depending on their relative load.