@Guineafowl in your post #30 you said
Now I have a feeling you are talking about the US "split phase" system here aren't you?
I meant a transformer with two poles in (at distribution voltage) and two out (at supply voltage). Before any connections are made onwards from the output, the terminals are exactly equivalent, neither live nor neutral. Just a plain old stepdown transformer. I’m in the UK, but was trying to generalise.
I think there has to be a clear distinction made here, because if I would do as you said "We ground/earth one terminal, and call that neutral." and the terminal I grounded ended up being phase trust me there would be fireworks going on and magic smoke (hopefully not from my burning flesh)
Back up a little here, and consider the transformer with its unconnected secondary. Remember that neither terminal is yet phase or neutral, just equivalent AC poles. Whichever one you choose to ground will become neutral by definition. If you then decide to connect the other (now phase) to ground, as you say there will be fireworks, but you wouldn’t. Why? Because now the live/neutral safety system has been imposed on the supply, the wire colours show you which is which.
In the US you have a transformer with a center tap and two secondary outputs so essentially an "isolation transformer" so you can maybe indeed take one of the legs of that transformer's secondary winding and ground it while the other then becomes the 120v potential.
As I say, not in the US but I believe they have three secondaries, the centre of which is grounded and becomes the neutral. The country specifics are not important, as the principle of L/N still apply there.
Here in Europe and especially in my country we have a 20kV to 0.4kV (3 phase 400v) (I believe the same goes on in UK etc)distribution system , so most private houses and especially highrise apartments are fed from the nearest distribution transformer which is not like the small pole pig transformers in US but instead a large house like facility with a big transformer inside, this transformer simply transforms the 20kV city/suburban 3 phase voltage to 400v 3 phase and adds a neutral.
Now if I have (which I do) in my apartment a single phase supply that means that my supply is nothing more than the neutral (taken from the distribution transformers neutral) and a single phase (which is one of the phases from the distribution transformer)
This means that the phase is always live and always phase with 240v in the wire no matter what you do about it, and the neutral is always neutral. There is no mixing of them, and if someone does indeed ground the phase he either blows his fuses or blows himself.!
My house is supplied with three phase 400V, with the neutral taken from the star point just as you describe. However, the OP was about a common confusion with polarity of AC. I avoided tackling three phase and country-specific systems in general as this can be confusing - I feel the principle of the L/N system can be more easily understood by starting with a simple two-in, two-out transformer. This way, we can see how it’s a connection system that we impose on the supply, not something inherent in the AC itself.
In my apartment block like in most others we have incoming 3 phase 400v with a neutral so 4 wires and then to spread out the load evenly each apartment is connected to a different phase but the same neutral.
So If I was to measure between live in my socket and live in my neighbors socket I would see 400v which is the voltage between two phases.
Our EU system doesn't allow any messing around and mistakes , people get fried easily with these voltages and currents.
It IS a good system!