[cachagua]

That is even vaguely true.

I apologize; I intended to be anything but vague.

The frame un-flexes when the load shifts from right to left. And that happens without the pedal forces going to zero.

Who said anything about the pedal force going to zero? All I said was it has to drop from its maximum.

What's getting left out of your analysis is that there are actually two ways for the frame to store some pedaling energy - by lowering the chainring (right pedal load), or raising the chainring (left pedal load). Moving between them is when the stored energy is pushed down the stays.

In other words, what we see when the BB "sways" from one side to the other and back? Again: the inertia at the rear wheel is pushing harder than your pedals, because your pedaling force has decreased in relation. In response to the decreased force at the pedals, the frame discharges some of its strain energy as we see, but there ain't no way that can get out the back wheel and move you along the road. The softer push is not going to overcome the harder one. Do you dispute that?

I don't know how I can make this simpler. If you and I push our hands together and push equally hard, our hands will stay still. If you relax a little and push softer, and I keep on pushing just as hard, will our hands move toward me as a result?

All the various static examples are demonstrating is that the flex is still in line with the drivetrain, and isn't just flying out into space. Then you take that understanding and apply it to the fact that the tension on the chain never goes to zero and the BB flex automatically alternates from right-to-neutral-to-left.

Flex is in line with the drivetrain -- not sure what you mean. Does it matter?
Tension on the chain never goes to zero -- doesn't need to; not part of my account.
BB flex alternates from right to neutral to left -- okay, if it goes back to neutral in the middle then manifestly there's nothing carried over to the next pedal stroke.