Polarity is still essential with AC circuits. The problem is that it is changing constantly, but in a predictable manner, whereas the polarity in a DC circuit is fixed.
The way to deal with that is to think in terms of a frozen moment in time, rather than a continuous fixed picture. Let's say, for example, that we pick the specific time along one cycle of the voltage sine wave where the voltage relative to Neutral is actually +120 V at the L1 end of the winding. At that frozen time, the voltage at L2 relative to Neutral is - 120 V. Thus, if we have connected a load from L1 to Neutral it is experiencing 120 V across it and an appropriate current is flowing with electrons flowing from the Neutral through the load to the L1 terminal. At exactly the same time if we were to connect an identical load from Neutral to L2, it also would experience 120 V across it and a corresponding current flow. But in this device the electron flow would be from L2 to Neutral. At the Neutral terminal, exactly the same number of electrons per microsecond would arrive from the L2 side load as leave going to the L1 side load. In other words, there actually would be no net current flowing between our external Neutral terminal and the centre tap of the transformer.
Now, suppose that the load we wish to connect really is two heating elements each designed to operate on 120 V, and connected in series so that we get the heat of both heaters coming off. We might do this for the heating system inside an electric water heater, or for a stove-top element. But now we realize that we really are not using the connections between each heater and the Neutral terminal. We can eliminate that connection entirely, and just keep a connection between the ends of the two heaters. That actually frees us to re-design the system so it's only ONE heating element twice as long as each of the original units, and thus able to work properly if supplied with 240 V across it. Electrically this new design will function exactly like our old two-elements-in-series design, but it will be simpler and it will NOT require any Neutral connection at all.
Now, back to our frozen moment in time. But first, I have to correct an error in your drawing from Monday, in the way you depicted the sine waves on the Output side. I am assuming you meant that the highest positive voltage at the top end of the winding is where that upper (blue line) sine wave peaks, and it returns to zero when the input side sine wave also reaches zero. But after that, as the input sine wave continues into the negative region, the output voltage at the top terminal keeps on going down until it reaches a maximum negative voltage equal to the previous positive voltage. Similarly, the red line indicating the voltage on the bottom end of the winding does the same thing, except that its voltage at all times is exactly the opposite polarity of the one at the top. The voltages at each end do not swing only from max to zero. In each case they swing the full span from zero, up to max positive, down through zero again, down further to max negative, and back up through zero again to continue. Its just that the two lines are mirror images of each other and cross each other at zero twice each cycle of the wave.
With that in mind, let's pick a different time moment to freeze the view. In particular, let's pick the moment exactly one half of the period of the sine wave later than our first moment. In a 60 Hz power distribution system, this will be exactly 1/120th of a second later. Now we find that the voltage on the top end (L1 terminal) has changed to -120 V, and the voltage on the bottom end (L2) is + 120 V. Again, each terminal has a voltage difference from Neutral of 120 V, but this time the polarity is opposite. For the hypothetical heating element load I described, that makes no difference at all. However, if it had been an AC motor, that would make a BIG difference, which is why AC motors are designed quite differently from DC ones.
We could go on and choose several points in time for a series of frozen views. At each time we would see a different voltage at L1 and L2 with respect to Neutral, but they always would be the same in magnitude, but opposite in polarity.