To simplify this: why is the following true yet my statement is false? Here are the currents measured at the panel, and the loads are all single phase L-N loads:
10A ... 10B ... 0C ... 10N
10A ... 10B ... 10C ... 0N
Because you stated:
...With single phase, the current leaving L1 is seeking L2, and the only path there is through the windings of the transformer between N and L2.
...
That is why if you have a 10A load from A-N, and a 10A load from B-N, then 10A will travel on the neutral; that 10A is seeking C, and the shortest path there is to N, then on to C through the transformer windings.
The A & B currents seek A & B. Once the current reaches the winding through N, they will NEVER try to get to C. They have no interest in reaching C through the winding. They want to get back to their source. There is no "on to C" through the transformer winding.
I am saying that if you are starting with a three phase source, current will opt for the phase instead of the neutral.
Only for a complementary load on the other phase. If the load on the other phase is not complementary, the current travels on the neutral instead, even if the other phase is present.
I describe this as I have for simplification. Why is it wildly inaccurate? Obviously, if you start with a single phase source, there are no Bs or Cs, so I'm not understanding your objection.
It is your assumption that C will be used and that A & B currents will seek C through the winding once they reach the winding through N. The OP scenario had a load on A & B with neutral current. The premise was that the neutral current wanted to get to C. That is simply not the way it works. The only way C gets involved is if there is a complementary load on C, otherwise C is not part of the in the circuit path for the A & B currents.
Think of truck hauls as an illustration: If truck A makes a haul, think of the delivery route as phase A, and the back-haul route as the neutral. Then consider that the only way truck B gets involved with A's route is if B makes a delivery and can share in the back-haul. With no complementary load on B, A is on its own.
By complementary, consider that a pick-up truck and semi truck would not fully share back-hauls. The pick-up may carry some load, but just because the pick-up route exists does not mean it will fully share in the back-haul. For the circuit, unbalanced load current will flow on the neutral even if all three loads have the same amps. Only if they are balanced loads will the neutral have no current.
Now let trucks A & B be doing their thing and sharing back-haul routes (the original premise). Truck C does not get involved in the A & B hauls unless C has a complementary load route.
Current returns to the source. A currents want to get back to A, B to B, and C to C and that is just the way it is. Unless there is an equivalent load on C that will allow it to share in the back-haul, the A & B currents will not try to get to C through the winding via N as was stated in the OP.
C is not involved unless it has a load of its own. AND IT HAS TO BE A COMPLIMENTARY LOAD OR IT WILL NOT SHARE IN THE BACK-HAUL. If the loads are not matched, then the shared current burden starts to divert away from C.
The OP premise was that the 10 amp loads on A & B resulted in a 10 amp neutral current and that current wanted to get to C by going back on N and through the winding to C. That is completely wrong. Those currents have no desire to get to C as they only want to get back to their sources A&B. C is not in the circuit.
If you want C in the circuit, then put a load on C that equals A & B loads and then C will share the back-haul.
Now Iwire proposed that just because he dumby "got between" C and A or "got between" C and B that he has now created a path and A & B current will flow through him to reach C. His load will differ from the loads connected to A & B so the A & B resultant neutral current will not disappear and seek C through him.
First, it is not seeking C, it is seeking A & B. Second, only if his load complements the A & B loads will he & C share in the current path back-haul to A & B. Thirdly, even if he shares some back-haul through C, he probably won't fully share in the back-haul so the residual A & B current will get back to A & B through the N path, not C. That residual current has no interest in finding C through the windings of the transformer between N and L2. Once it reaches the winding at the N point, it will only go through the A-N winding to A and B-N winding to B. It will NEVER go through the C-N winding to reach C.
Edit: if you are taking issue with this because if you wire some kind of open transformer source, current will behave in a certain way because you're using A and B and there is no C, I would question the relevance to 99% of the systems an electrician will see and wire in the field.
Just because C is there does not mean C will be used. Without a complementary load on C, it is out of the picture.