Re leaving after your set, my rock band had a particular case of that the other day. We ended up closing the night after the headline band's drummer broke his arm, and three other bands were drafted in to play before us. Trouble is that two of the bands were all under-18s, so they and their parents stayed until about 10pm and then left before we started, which didn't leave a whole lot of audience behind for us. :-/
I think it's less common in singarounds or open-mics, because people have usually come for the entire evening. Still happens, but less often. Sometimes people will stay outside the main "circle" (or however the place is arranged) and chat at the bar, then come in for their go, then head back to the bar again. Doesn't always mean they're not listening.
Chris, that poem/beat thing is fun - thanks for the reference. (Vid and music are on Youtube, for anyone who wants to look/listen.)