You're right, very interesting.
We have never used click tracks except for the scant few times we recorded. BUT.... I have tried to get my band to use one simply for intros into some of our songs... and that because we have a few songs in which our lead guitar player varies the tempo so much that it's shocking.
He and I have fought over tempo more than any other thing... he tends to hear, (in his head), a much to slow tempo for songs he's not really fond of, and extremely too fast tempo's for those songs he loves. And the difference in tempo can be remarkable. I'll give you an example:
We play a song, (which song isn't important here), that was recorded at 148 beats per minute (approx). I know this because I used a metronome app to show him how off he was. I recorded his intro during a practice using my phone. He swore I was full of #$@# and that the song was played at the tempo he started it at....
So I replayed his intro with my phone and had the metronome displaying his tempo.... 115 beats per minute... I'm sure you know... MUCH too slow. HUGE, ENORMOUS, in fact... damn near like making Through The Fire And Flames a waltz.
What was his reply? "Well, I like it better slower"... this after arguing that it was NOT slower and the actual tempo. I could have killed him.
now in fairness we do very tempo for several songs because we're mainly a dance band... for middle aged and older crowds. But a 30+ beats per minute difference? It's not even the same song anymore.