Thanks for the clarification. Now I understand!
I’m not sure that all artists would agree that moving the listener is their top priority, though. We creatives tend to be extremely critical of our work so I’d venture that most artists aim to please themselves first and foremost.
In terms of playing music in a group situation, the highest reward may vary from player to player but for many (including me), those moments when everyone is locked in together and the music becomes a channel for a mysterious power that "appears out of nowhere" and dramatically ups the intensity level is something familiar to many players although they may not be able to name it.
The Grateful Dead coined the phrase "the music plays the band" to refer to this phenomena and it seems as good as any. Once experienced, it’s unmistakable and when musicians access this state, there’s no way the audience won’t be swept along.
I don’t know your musical tastes, but my first exposure to this as a listener was when I was in high school, courtesy of the Allman Brothers Live at Fillmore East album, particularly Whipping Post and Elisabeth Reed. There are, of course, many many other examples. I’ve certainly experienced this with live Jazz, especially with the Dave Holland Quintet. I’m not much of a Classical fan, so I can’t speak about how this might manifest in this genre.
As a listener, my top priority is emotional engagement, so I can relate to the value you place on this.