David killed Goliath with a sling and a rock right? Historians describe that sling as two cords with a leather pouch between them. I think they left out a small detail, probably deliberately.
When I was a kid I made one just like that. I tried many times to find a way to launch a rock from that sling with any amount of power. I swung it around my head and yeah you can throw a rock with it but not much harder than you could throw it by hand. Then one day I guess I was 12 or 13 yrs old I was watching a movie on TV. It was set in ancient times when they laid seige to a city and bombarded it with rocks fired from a trebuchet. That was when it dawned on me. No wonder my sling weapon was no good, it was missing a critical part! It should have had a stick like the arm of the trebuchet!! I said holy shit im gonna try that so I ran outside to the tool shed and tied the two cords of my old sling to the end of an old broom handle. I put a rock in the sling and I was holding the broom handle, knew right then, as I could feel the weight hanging off the other end, this was gonna do something. So I let it hang behind me and I swung it over my head and after a few attempts, holy shit. That rock shot out of the sling and across the field behind our house like a fuckin missile!! I was like hot damn!! So I experimented with different lengths of cord on the sling and different kinds of wood for the long handle. I found a slightly flexible wood worked really well if it made it whip a little it added extra power. I was launching rocks about the size of a baseball and they went a hell of a distance. A truly lethal weapon that if you think about it, would have actually been the precurser to the trebuchet not the other way around. Once someone invented the handheld version like I describe here, they just made them bigger and bigger until they ended up with the seige weapon size trebuchet.
Trebuchet: https://www.youtube.com/watch?v=9KCfs2KQKwI
Probably cause by the time engineering technology was good enough to make the compound bow parts the weapons market had aleady switched to gunpowder weapons.