John Coltrane's Tone Circle

On the bandstand, there's usually a ton of highly aware counting going on. 24 bars of rest! followed by 8 bars of rest! and then 16 bars of latin feel! now back to 8 of swing!

On top of that there is definitely some feel and intuition going on. But for a band to play non-trivial music, everyone is counting unless they know the material cold, and even then they are probably counting at times.

Indeed, as a long time fan of prog metal and tech death I'm quite aware of the importance of counting (and the existence of people whose counting abilities far surpass my own)!

But I think the quote is also referring to casual enjoyment of music where the counting might not be deliberate.

Right, I should have spelled that out - the listener gets to count subconsciously only because the players are counting very consciously.

Playing music has changed my listening, and not necessarily for the better. I'm sometimes counting or listening for structural and composition elements in a way that can be distracting from just enjoying the sound/vibe.