Yes, the only loss in energy with the frame flexing back and forth is from elastic hysteresis, which is very low for metals and carbon, compared to say an elastomer, where hysteresis can be quite significant.

It is a very small energy loss in absolute terms, never mind trying to compare the delta loss between two bike frames of slightly different stiffness. You would be pissing in the wind attempting to measure it!

There is a lot of BS talked about frame stiffness vs power transmission. At the end of the day if you put out 500W at the pedals, you will measure approximately 96-97% of that power at the rear hub due to drivetrain losses. So let’s say 480W at the rear hub. So how much of that 20W loss is likely due to frame flexing hysteresis? Let’s say for arguments sake it was as much as 5W. So if we then doubled the frame stiffness we might save 2.5W at a 500W output.

Frame stiffness is important, but not for raw power transmission. This idea of a stiffer frame transmitting more power to the wheel doesn’t really stack up with the physics.