Remember, only the secondary winding EMFs are equal, taking the winding IR drops into account, the transformer terminal voltages will be imbalanced too.
Yea, that’s why in the original discussion I said
My real world data, from several sites but mostly from my own home that shares a transformer with 5 other households, shows no observable movement of the center-tap voltage while local swings in my own home can be a couple of volts with a 10-15 Amp imbalance.
I’ve heard the theory that your neighbors imbalance can cause your voltage to move, but I have investigated that and find it is not measurable. I’m sure that a case can be found, but it is not a factor in well run networks, which is the rule here, not the exception.