Rami, I have much respect for your contributions to this site and I rarely disagree with your views - but in this case I do disagree. Like you, I've played drums for a very long time (40 plus years) and I have spent a lot of time trying to get my head around the concept of playing behind the beat vs. ahead of the beat - and I have carelfully analyzed hundreds of hours of studio recordings I've performed on and countless recordings of live performances. There indeed is such a thing as playing behind, ahead and on the beat. While it may not be a conscious approach, it is a feel that is inherent in most seasoned drummers.
While I do agree that if a drummer plays behind the beat for a whole song - then yes, it does simply establish the beat. However, as one example of behind the beat that can be heard in many recordings, often a drummer will play a little behind during a verse and then go a little ahead in a chorus (to gvie the song a lift) and then settle back into the groove.
Old R & B has behind the beat grooves all over the place. Many ballads use the behind the beat groove and then hit the beat more agreesively in the chorus, etc.
I'm not talking about straying or dragging or rushing - I'm talking about manipulating the groove. I've olayed a lot of R & B, funk & "soft jazz" and I manipulate the groove all the time - and if I'm working with good players, they also know how to fall into that groove and then jump out of it when needed.
Now some genres (harder rock, punk, speed metal, etc.) tend to push the groove so the behind the beat feel is not as common. Although you can hear it very clearly in much of the early Sabbeth recordings.
Regarding playing to a click - rarely (if at all) can a drummer consistantly play on the click - both because it is rare that someone has that level of technique and because each person's feel and interpretation of the groove varies. In fact when drummers (or any musician) gets so anal as to focus that intensely on the click - they then become a slave to the click and the performance suffers.
Music needs to breath - playing ahead and behind the beat (at approriate places within a song) - is was allows the music to breath - and makes the difference between music with a fell vs. programed beats that are more technology than art.