To be fair, slings were incredibly deadly killing machines and were only outclassed due to a bows[s] superior range[/s](Sike, just looked that up, they outranged bows prior to the invention of the english longbow)  ease to use.

The Romans even invented a tool specifically designed for removing lead sling bullets from fallen soldiers...

Adding to this because I have a huge inexplicable attachment to slings (Damn you total war)
-Bows are easier to use in dense foliage 
-Bows are much, much easier to learn how to use
-When used in formation Archers can be clumped while slingmen must be spread out, resulting in a less massed volley.
-Slings are even more physically intensive than bows.

however slings worked incredibly well against armored (or unarmored) targets

TL:DR- David vs Goliath was rigged from the start