But the statement that "rotational weight counts double" is not exactly a "nonsensical idea" since it actually is counted "double" in the math...even though it does not apparently end up making the bike faster.
Indeed, mathematically it counts double but then get's evened out by sideeffects. But that's not what was being put forward:
Ozrider, since 600gms of that weight is rotatonal (wheels) you cant multiply that by 2 (1200gms) and the remainder of the 1500gms is static (900gms). In effect it' equates to 2100gms(2.1kgs) difference if the weight was static which is a significant amount considering upper end bikes are circa 7kgs
That's quite simply so missleading it's just nonsense.
Now to your hypothesis: This is not
supported by the analysis, as that outcome actually indicates it's so small an effect that you hardly will notice it. This is pacelining which gives very minor speed jumps for very, very short periods. And to make that one even more apparent... we are talking loosing the group which means all meters are far in the red. At that moment we can notice a difference which for all purposes is unnoticeable?
Somehow people have this idea that a cyclist has much larger accelerations than we actually have. The forces involved are minor.
So the light bike effect is psychological for sure... PLACEBO. As with any of these things I'm certain a double blind test will show that it's all in between the ears. This has been shown by frame materials too, something which people still maintain they can feel.
=> Still talking Paceline, not talking climbing.
So to sum up: A lighter bike with same aerodynamic properties is a bit faster on the flats, but this is extremely minor. The reported differences are nowhere near what is supported by math. Weight at the rim or at the frame also doesn't really matter, it's the total weight that counts. Lastly, even Cavendish has a minor acceleration all things involved. That's not to downplay cycling, it's just how it works. Mass and acceleration are pretty small things in the whole picture (that changes quite a bit when climbing ofc).