Originally Posted by Maelochs

Seems simple enough to me .... the motion of the crank translates the motion of the foot into motion of the chain and ultimately, the rear wheel, which propels the bike forward. Anything in the system which transfers energy anywhere not alo0ng the perfect (circular) path of the crank, wastes propulsive energy.

Think about a bike with really loose bottom bracket bearings, or cranks which weren't tight to the spindle---no one would be trying to convince anyone else that those things in some way returned energy to the bike because "ya know, conservation of energy." If the whole frame flexes at the bottom bracket, same effect---some of the potential propulsive energy goes in different directions. When the frames snaps back (or is pushed back by the other crank) it is still lateral, not longitudinal motion, and this does Not help propel the bike.

it's going Sideways, people. Unless you want your bike to go sideways , any sideways motion is wasted, since "wasted" in this case means "not propelling the bike forward."

The only way the bike could be acting as a spring and propelling itself forward with energy from deflection would be if the bottom bracket twisted longitudinally under load---but that would imply a fixed or high-friction crank bearing.

Think about it .... if your wheel shakes from side to side really badly, are you going to claim that its okay, because the energy lost will be returned and help propel the bike forward.?

For maximum efficiency, everything has to stay in the plane in which it is meant to operate. Every angular flax is a waste of energy. Y'all are engineers with degrees and all that ....

Ask the race-car engineer: Is frame flax a good thing? Does it make the car go faster? No ... eventually it breaks drivetrains because all those drivetrain parts are designed to work in very specific relative orientations. The forces involved with automobile engines are so large that transmissions will explode, gears will strip, cranks will snap .... the forces involved with cycling are so puny that realy almost nothing happens ... which I think was the OP's point, he just said it badly.