No, not really. Sling bullets lose force quite fast. Unless the guy you shoot at is standing only a few meters away from you sling bullets would do nothing against metal armor (which wasn't that rare in the later areas and you would see entire companies with field plate). Slings were phased out not because of aesthetic reasons or because they are "peasant weapons" (a lot of peasant weapons got adapted when they proved effective) but because they simply couldn't keep up the arms race. Bows were made stronger (medieval bows are a lot different and stronger than what the ancient greeks and romans used) and the arrows could be adapted to deal with armor. For slings such advancements were impossible. Slings hit the end of the line once iron armor became common while other weapons still could be improved.
It appears you are mostly correct, and I was incorrect. The Sling was the victim of advances in warefare. It is easier to quote
http://chrisharrison.net/index.php/Research/Sling
When looking at the evolution of ranged weapons, there is a trend towards increasingly simple operation. The sling requires enormous skill, one that can generally only be obtained with training from childhood (Hawkins, 1847; Korfmann, 1973; Wise, 1976; Ferrill, 1985). Without this mastery, a person armed with the weapon would be practically useless. The sling is exceptionally difficult to aim because it is being rotated when fired. It is common for people to fire projectiles backwards when they are first learning, meaning a high degree of proficiency is needed before they can be safely placed in a battlefield situation. On the other hand, the bow could be taught at any point in life, and be deadly with minimal experience. The bow does not suffer from the sling’s accuracy problems because of its ability to be drawn and then aimed. However, archers did have to be strong, which increased the required training time (Wise, 1976). The development of the crossbow with a mechanical device to cock the weapon enabled anyone to use it and have the ability to kill even an armored soldier at distance. The crossbow was the first true ‘point-and-shoot’ weapon, as it could be cocked and then easily aimed using the large stock. Although much slower to reload than bows, it was seen as an acceptable tradeoff for the ease-of-use gained. The shift to firearms was similar. They were even slower than the already sluggish crossbow, at least at first. However, the operation was simple and there was no physical strength needed to load the weapon. Also, its ‘point-and-shoot’ nature made someone with almost no experience immediately useful on the battlefield, and very deadly. This evolution occurred primarily because of changes in military and governmental organization. In feudal times, lords could recruit their serf population as soldiers (Wise, 1976). Many of these men were already proficient with the bow or sling, which were used for hunting game. However, by the High Middle Ages, nations and cities had developed large standing armies, which were recruited, sustained, and equipped by the government (Martin, 1968). An increasing number of these recruits were from urban populations which had far less exposure to ranged weapons. These units had to be trained from scratch and there was a high turnover. This led to the increased use of weapons that were deadlier with less training. The sling was perhaps the least effective choice of ranged weapon in this role.
The style of warfare in medieval times changed as well. There was a progressively better military organization and leadership structure, causing the direction and deployment of troops to be much tighter and more integrated. Compact groups of homogenous units became increasingly prevalent during the medieval period (Ferrill, 1985). Because of the rotational action required to cast a projectile, the sling required considerable space to operate effectively. Armies of antiquity, like the Greeks, used slingers as highly mobile and loosely structured skirmishers. It would have been troublesome to pack multiple rows of slingers into a typical medieval assemblage, where each soldier would fire over the row in front of them. Even a slight misfire, launched in front but too low, could cause friendly casualties. Archers could simply point upwards, over their fellow soldiers’ heads, and could be formed into relatively dense formations. Soldiers equipped with crossbows or firearms could also be closely grouped.
Ranged attacks work especially well in volleys, as the concentrated firepower is likely to wound more people simultaneously, causing confusion and fear, and making it harder to regroup. A group of archers could draw their bows and fire simultaneously. Crossbows and firearms could do this even better. The sling was much harder to coordinate as the arming, aiming, and firing of the weapon was a single motion. People with different length arms and casting styles would fire at different moments, even if starting at the same time.
More cohesive and robust economies in later medieval times lead to a surge in castle and fortification building. This meant that armies were increasingly placed in siege situations instead of face-to-face on a battlefield. The sling was an important siege weapon in antiquity. Its high rate of fire, accuracy, arching trajectory, and versatile payload made it extremely effective. (Wise, 1974; Ferrill, 1985; Grunfeld, 1996; Bradbury, 2004) However, as the style of siege warfare matured, so did the architecture of the fortifications. Bombardment by slings became less and less effective because units were garrisoned in fortified positions. The premier armaments in these battles were heavy weapons, like trebuchets and cannons, which were able to pulverize defenses so infantry could attack. Also, newer fortifications sported special slits for ranged units (bows, crossbows, firearms), allowing them to fire from protected sniping positions (DeVries, 1956). Soldiers could draw or cock their weapon in safety, and poke the tip out of the opening. Even an experienced slinger would have great trouble firing through a thin slit or hole in a cramped chamber, let alone hit an enemy. Firing from the castle ramparts would be an equally dangerous affair for a slinger. A crossbowman or rifleman could fire from a crouched, leaning or prone position, exposing very little to the enemy’s ranged units. However, a slinger must stand, and have room to get a powerful and accurate shot. This made slingers considerably more vulnerable. Furthermore, castles had limited room on their ramparts, towers, and other defensive structures. It was vital to pack as many ranged defenders into this area as possible to repel the enemy. Since slingers required more room to operate than other ranged troops, they were rarely used in defense.
Advances in armor design were perhaps the sling’s biggest obstacle. In the early middle ages, it was common for infantry to carry a shield but wear little or no armor at all (DeVries, 1956; Martin, 1968; Nicholson, 2004). The sling would have been effective against these troops. However, by the High Middle Ages, advances in metallurgy and production meant more advanced armor was being used by knights and in greater quantity (Bradbury, 2004; Nicholson, 2004). These improvements trickled down to the common foot soldier. The formation of national or city militias meant that taxes could fund troop equipment, drastically raising the average level of armor in European armies (Martin, 1968). Plate armor became increasingly prevalent during the 1300s. By the 15th century, entire suits of plate mail were used by knights. (Blair, 1958; Nicholson, 2004) While a sling projectile has considerable impact energy, plate armor was often designed to deflect hits, reducing and redirecting the force. In addition, soldiers would wear gambesons and other padded clothes underneath their armor to diffuse the force of an impact. These new innovations made the sling ineffective. Although tipped projectiles were better suited at penetration, even archers and crossbowmen had difficulty with plate armor, which ultimately lead to the widespread adoption of firearms.
But in the fantasy word, I would think warfare may be a bit different, as magic and monsters may change things. Small groups of adventurers would be okay with the amount of space a sling takes up, and with monsters some societies would need weapons to defend. Or maybe not. But ultimately, i'm planning to see how my group will react to the new ranges and damage of the sling I suggested.
