It only doesn't cancel in a four wire system with 90 degree phase angle.
It does cancel just like three phase if you have two symmetrical phases 180 degrees apart (this is exactly what happens with 120/240 split phase systems) as illustrated below: (however this arrangement does not give continuous power as three phases do)
I agree, the 180 degree case ("split phase" or whatever you want to call it) will reduce/cancel the neutral current. It is possible to run a three wire 90 degree two phase system - this will reduce the current in the neutral, but cannot cancel it entirely (down from 2 * Ip to 1.4142 * Ip IIRC)
I am still thinking about the phase relationship in a center tapped transformer, if you think of the ac power as a rotating battery or rather in this case a pair of rotating batteries going around so first you have positive on top and then negative, if you have a connection between each cell as well as one at the positive and one at the negative you get V1 and V2 you can either run a load at V1 or V2 or a load at V1+V2 now if one of the batteries was 180 degrees out in polarity compared to the other you could still load them at V1 or V2 but if you connected so that you had V1+V2 you would now have positive connected to positive with the result that no power would flow.
The situation as you describe is correct for the first half-cycle G7PSK.(middle circuit diagram). In this state, there is already effectively 180 degrees phase shift, because one supply has its 'negative'/neutral connected to the common neutral, while the other one has its 'positive'/phase connected. On the second half cycle, V2 reverses polarity, as you have drawn in your bottom circuit. But V1 also reverses, so the voltages still sum.
Also if you think about the current flow as generated by the magnetic field in the transformer and apply the hand rule to that you realise that unless one half of the center tapped transformer is wound in the opposite direction from the other the power has to all flow in one direction. so the bottom leg at any one moment is at one potential the middle is at a higher potential than the bottom leg but lower than the top leg
It's not so much a matter of the direction they are wound in, as the way they are connected. One method of manufacture is to wind half of the secondary and bring the wire out to a tap. Then, without cutting the wire, take it back and keep winding the other half of the secondary in the same direction.
Alternatively, you can just have two separate and identical secondaries (possibly both wound at the same time), giving you four ends of the windings. Two of these are connected together, and depending on which two, the voltage at the ends of the combined winding will either add or cancel.
Anyway, it appears that the discussion has been sidetracked into the benefits of various earthing systems. All we need now is for someone to come out in favour of using a floating distribution system, and the sparks will really start to fly!