We’re all good Zank, but thanks.

Re: racing cars, etc. – with such hi frequency power delivery I don’t see an analogous situation as it relates to propulsion. Bicycles have low frequency power delivery with very distinct times of power, vs. no power. I think that’s what opens the door to the possibility of power smoothing and max muscle fiber tension reduction from strain energy flow. Ultimately I think it resolves to some sort of spring/mass/inertial system with different spring constants (the frame), different masses (bike + rider) and different forcing functions (rider power delivery). As I noted earlier – the flexural modes that could influence the drivetrain aren’t as intuitively obvious as for, say, a golf club. If you're a serious golfer or fisherperson, you're probably aware of the degree to which strain energy affects performance. If not, try out the stiffest club or rod you can find.

I mentally resolve the main triangle as a single beam (a spring that flexes in all three Cartesian planes); BB at on end, handlebars at the other. Rider, out of the saddle, honks down on the power and you can imagine the deflection, a deviation ‘twixt chainwheel and the frame that increases with increasing force by the rider, with the chain being the constraint. You've experienced it. It’s a simplified notion, but it allows me to imagine a way in which power pulses and deflections, at a particular frequency for a particular system comprised of all of those parts, could apply the strain energy back into the chain in a way that would reduce peak chain tension while broadening the crank-angle/period of delivery. For the same amount of energy (and power delivery), lower max chain tension but delivered over a longer period of time. Seems a physically reasonable proposition to me, and if it does exist it would have to alter the power delivery characteristics in ways that should be beneficial.

Imagine an ancient one lung IC engine with something like one power cycle every second, connected to a stretchless cable, hauling a boulder up in the air. The cable is going to see high peak tensions corresponding to the power cycles. Now stick a spring in-between the rock and cable, and ignore the harmonics that would probably cause havoc (or else give the air a meaningful viscosity); intuitively you can tell that the maximum loads on the cable (our cyclist’s legs) would be much reduced. Intuitively, the efficiency with which the boulder was hauled up into the air would have to be more efficient since energy isn’t being wasted on constantly accelerating the rock after each non-power cycle. Spring systems were used for power smoothing in industrial drive applications like this back when motors were crude.

But: It’s a spring that’s operating over a relatively small range of deflections, so one would expect small results, nothing enormously obvious.

I played lots of paddle ball, with a (essentially non deforming) wooden paddle, a long time ago. When I switched to racquet ball I wasn't any stronger by by gawd the ball went a hell of a lot faster. It was hugely obvious, and totally down to the strain energy of the strings and racquet acting on the ball.