Chris said:

Butt makes a difference in feel, not play. Any difference in play can safely be written off as being due to placebo effect.

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"difference in feel" is the side effect of difference in energy transfer.
it's really easy to test, just grab a few cues and do some lag shots, try to keep the same stroke and speed and let us know it the CB always traveled the same distance.
I might be impossible for a human to stroke at the same speed over and over, so maybe find a robot to do it.
Or I can save you the trouble and tell you, the butt makes a difference!!

Chris said:

The cueball is already gone by the time any vibrational waves travel back from the butt to the tip. The cueball doesn't "know" anything about the construction of the butt, whether it's made from cocobolo, bacote, purpleheart, or a broom handle. The butt has a large effect on the feel for the player, but it has zero effect on cueball movement. To credibly claim otherwise, one would need to explain how information about the butt made it back to the cueball during the hit.

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it's the same argument like for CF that is more powerful. it's about energy transfer.
Butts makes a different! both in energy transfer and deflection.
All you have to do to test it is grab a few cues with different construction methods and different woods, with the same joint so you can use the exact same shaft and run a few test hits and realize that the butt makes a difference in the hit and if you are able to stroke over and over with very similar speed, you'll see that the ball moves differently. and if the stroke is the same, the joint is the same, the shaft and tip are the same, then it has to be the butt.