I couldn't imagine Miles' Blackhawk sessions without all the ambient noise. The sounds of the audience, the cash register, even the drink blender just add to the live aspect IMHO.
Occasionally I've experienced performances where a very subtle and seamless transition from one soloist to the next made applause seem inappropriate, and no one made a sound. When you can get an audience to be silent through musical means, those are special moments.
I played a gig once where a guy and his party sat close to the band and talked loudly all evening. Both the clubowner and the band asked him to keep it down, or maybe move to a table at the other end of the club, but it didn't do much good. He finally left while we were in the middle of a tune ( but not before flipping the band the finger). Now I tend not to be overly confrontational, but this pissed me off so much I put down my horn and followed him outside and confronted him. He was very surprised to see me and backed down, which was good because I hadn't thoroughly thought out my next step. It wouldn't do me much good to get my teeth knocked in.