Not sure if this has already been mentioned, but many environments are actually fairly rich with improvised weapons. Yet I can't recall reading of an incident where people have thrown hard objects, swung hard objects, etc when rushing a shooter.
I knew guys in high school and college who'd start a fight by throwing car keys in somebody's face, or flicking a cigarette lighter towards somebody's face. The distraction usually let them land a few good punches and/or kicks before the other person could react.
(I'm not advocating this for normal social encounters; just saying that there are all sorts of things out there - from pots full of hot coffee, to ketchup bottles, to car keys - that could be put to use in a pinch, with the right mind-set.)