From the link that you posted
"The final decision rests with the TSA officer on whether an item is allowed through the checkpoin" .
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It's common knowledge you cannot bring cues on a plane. The "final decision" comment is there because it's at the bottom of each page and it is there to give the power to the officer on the spot so it does not become major ordeal - meaning it should all end right there on the spot, not available to go "up the ladder".
Also, you wrote - "When leaving from the US it's sometimes a problem, depending on the airport and security people. I do think if it's broken down and inside your carry on, no one would bat an eye."
First sentence says it's "sometimes" a problem and the second sentence says "I do think if it's broken down....no one would bat an eye".
Which one is it? Have attempted it and been thwarted or have you never tried it?
All that being said - pics or didn't happen - bring a cue on a plane and take a picture. Otherwise, I would recommend you do not give recommendations for people to bring pool cues on planes.
FYI - I've been playing since the 80's and I've flown nearly a million miles.