Don’t be confused. It’s usually necessary to involve your upper body to ride a vendetta mbb though some skilled pilots can indeed ride no hands.
So you either believe that upper body involvement contributes to forward momentum or it does not.
Might I suggest the yes camp are all but one.
You might suggest that, but only if you want to provide a textbook example of an
argumentum ad populum fallacy. At the risk of pointing out the obvious, a false claim would be false even if everyone believed it to be true. A true claim would be true even if everyone believed it to be false. Someone may have good reasons for holding a false belief, and someone may have bad reasons for holding a true belief. Perhaps that's because whether a claim happens to be true or false has nothing to do with belief.
If you believe it does not then you may as well ride a fixed boom machine and not waste energy pulling pushing your bars around a pivot point.
Except that there are perfectly good reasons to prefer a Cruzbike to a fixed boom recumbent which are completely independent of whether the claim concerning handlebar wagging is true. Do we expend more energy riding an MBB than a fixed boom recumbent. Absolutely. Is energy conservation all that matters when deciding what to ride? Absolutely not. If it were, I'd be spending all my time riding my fixed boom bents, and I certainly wouldn't be spending any time riding my road bike.
Of course upper body involvement does help propel the bike forward and is fundamental to the platform.
What else is my upper body doing if not........... spin drying the dirty washing. Please.
The only obvious effect of moving the handlebars is that it causes the bent to change direction. Anything beyond that is, so far, just speculation buttressed by bad arguments, bad evidence, and bias confirmation.
How much..... as much as 30% extra. For me no way. I’m built like a cyclist.
But it’s real and works. Especially at lower effort and cadence.
And the proof of that would be? Oh wait, there isn't any, it's just an argument by assertion. As rational individuals, we can and should try to do better than that. Or we can focus instead on the things that Cruzbikes demonstrably do better than fixed boom recumbents, like eliminating the problem of heel strikes in tight turns, chain interference with the front wheel, and power losses resulting from an idler wheel and/or guide tubes. To the list I would also add the advantage of being able to set pedal reach and pedal height independently without having to move the seat up and down the frame (eg: Bacchettas, Rans, and Schlitter recumbents). All of these things hold true whether or not swinging the handlebars in a particular way adds any power to your pedal strokes.