But wouldn't that shot/pebble-like-stuff fall and potentially hurt someone?
I don't think that birdshot is dangerous on the way back down, unless a pellet falls right into your upturned eye. It has enough kinetic energy to harm a bird (or fragile drone) within some range of the shooter, but by the time it comes back down it has slowed to terminal velocity. Birdshot is only around a millimeter in diameter, like coarse sand. The "pebble-like-stuff" would be buckshot, which would not be practical to use against a bird/drone because not many pellets of that shot fit in a shell, making it pretty hard to actually hit a flying target with at least one pellet.
Despite the relative safety of falling birdshot, firing guns into the air in urban settings is generally frowned upon.