Slingers!
Hmmmm.......an interesting thread we have here, as I have long speculated on some of these matters, myself. Now I am certainly not any sort of "expert." In fact, I always say, " 'Expert' is spelled: E-G-G.....S-P-U-R-T!" So now that you've been warned, let's see.......in no particular order.......
First off, some years ago I took a bunch of Defense Tactics classes that were quite fascinating. Impact weapons were a major part of the "curriculum." Most people BADLY UNDERESTIMATE the effectiveness of blunt trauma ( impact .) Now it may be that it would be difficult to bring down a deer with a sling ( as the head is a small target and the body is resilient ) but this is not true for any number of smaller and slower animals, some of which tend to "freeze" when alarmed, making it easier for a skilled slinger. Thus the sling is the neolithic equivalent of the modern .22 rimfire, well suited for small game hunting, or the modern shotgun loaded with birdshot, as birds are VERY plentiful ( they tend to come in flocks! ) and very good eating.
Zwiebelteute, I think you are on the right track in considering economic factors and a cost/benefit analysis. The sling is easy to make and rocks are everywhere, thus even if it has limitations you are still better off with it than without it, because it has cost you so little to obtain a sling and stones. Note that historically arrows were expensive to make, whereas rocks can be had for free.
As far as warfare is concerned, let me again suggest that slingers may have been used in hurling massed volleys rather like the flintlock muskets of the 1700's. Of course arrows were used this way too ( English longbow ) but I suspect that a major factor was the widespread use of metal body armour, first chainmail, then plate, in medieval Europe, which would render the sling ineffective. If you go back to the early classical era, we know that at least some of the Greeks ( Xenophon and the 10,000 ) had bronze armor, but the Persians apparently did not, except maybe for a few "bigshots."
Some years ago I read a fascinating book called "War Before Civilization" where the author discusses many archaeological sites that show signs of attack and defence. Unfortunately, human beings are fragile and easy to damage, and easy to.......uh......."render permanently inoperative." Thus any weapon that can be used to hunt game can also be used against humans. But "that's the way the cookie crumbles."
Also let me welcome Subotai Ba Atur to the forum. Subotai, a handful of posts under your belt and you are already causing a ruckus.
Yup, I can see you're gonna fit right in around here!
.......Dan