Thanks for your thoughts. I am interested to know about your 'curious research'!
Terminology is important. 'Power' in slang is often used to describe the presence of a voltage, but its meaning is more akin to 'energy'. In electrical terms, power is current x voltage = Watts. To be pedantic 'power' does not 'go out' of the neutral. It is given up in the load being fed, and during this process current flows in both live and neutral (even that's a simplification of course, electrons bounce around, rather than 'flowing' en mass, but that's a whole other story!)
Your rope around a tree analogy generating heat works if you think of the distance moved by the rope as current, and tension in the rope as voltage. If you ignore the elasticity of the rope and change in dimensions of the tree (!), then the distance you pull the rope on one side is the same as the movement on the other. But the work you put into the pulling, (force x distance), is absorbed by friction at the tree, and if you were to measure the tension at the loose end of the rope, it will be less due to the tree absorbing some. At the extreme limit where the tree friction absorbs all your pulling, there is no tension on the far end of the rope, equivalent to no voltage on your neutral wire, and the scenario you describe in your first post, asking why the tester shows 0V on the neutral wire. But there is current flowing (movement of the rope). Yeah that's contrived, but go with the flow
.
Bearing in mind you are pulling alternately on each rope 50 times a second
Does that work for you?
PS not everything you read online is true (particularly on Quora
)