Mmm. Most typically, peltasts had javelins and not slings or bows.
I'd like to point out that peltasts didn't depend solely on their ranged weapons, but on their light weight equipment and loose formation. They were more free to move around the field than their heavier-armed and tighter-packed counterparts. As such they would typically move to short range and throw missiles at opposing hoplites and phalangites, disengaging if pursued. At the battle of Cunaxa, a body of peltasts allowed enemy cavalry to pass through their ranks, being able to move aside thanks to their agility, and throwing javelins into them as they passed.
I'm not familiar with Gaugamela, but from other battles in that period, the peltasts being used to screen Alexander's advance wouldn't have been a nice dense formation lobbing missiles at standoff range but rather a porous and chaotic mass. If you order horse to fight in such a way, their advantage of speed is negated. If Persians charged into the peltasts, they would have gone in like a knife through jello and then been harried by the agile light infantry hitting them from all sides.
Sort of losing the thread of the original point though, which was that slingers could be effectively trained to a high enough skill level to serve as soldiers in a useful amount of time. Certainly the shepherds, having ample time and motivation to practice the sling would be very good with it and your first choice if available... but I cannot believe that ONLY shepherds were chosen as slingers when there were thousands of such troops in an army of the day.
Time was I read about the battles of Alexander’s campaign into Persia in better detail than the Wiki article I quoted from gave. I agree with you about the peltaist meaning javaliner in general. I’m not sure peltaist is the right word to use here. Offhand I don’t remember what slingers were called back then. I do remember that at Gaugamela, Alexander used a lot of slingers to support his very difficult military tactic. Moving his cavalry to the right so that Darius was forced to respond, and then taking advantage of the soft spot Darius had opened in his own line. In this case the cavalry was the visible menace, with the light missile men concealed behind all those horses.
As for their engaging the Persian cavalry once Alexander made him move, if the Persian horsemen got involved in harrying the slingers and archers and javelin men, so much the better. Their whole point was to keep those heavy cavalry away from Alexander’s push towards capturing Darius. They didn’t even have to defeat the Persian horsemen; just keep them busy. If the cavalry spent their time futilely chasing the light infantry, the slingers were doing their job while Alexander did his.
I never said that shepherds were the only source of slingers. I do maintain that they were a great natural resource for the military to draw on when necessary. There was no need for kings or city custom to keep them practicing at the sling. It was in a shephard's own best interests to learn to use that light, inexpensive weapon from his daddy, and keep in practice with it. Well into the middle ages, shepherds were a self trained body of available manpower. If some warlord could draw on other populations who also practiced the art, such as the Balearic slingers, that was gravy.
Speaking of dodging aside from a charging cavalryman, the Macedonian phalanx did one better. Two better, actually. Before meeting Alexander, Darius had high hopes for breaking up the upstart Hellene infantry with war elephants and scythed chariots. Elephants were always chancy, and as likely to savage the troops on their own side as the enemy. Scythed chariots were a different story. For centuries they had been the super weapon of the Near East.
Alexander’s phalanxes must have been superbly trained. They dodged aside from the elephants, leaving them a clear pathway to run through—which the elephants took. How they managed this, as tightly packed as the Macedonian phalanx was, is more than I can tell you. The scythed chariots were a different matter. The phalanx seemed to respond the same way—dodging to the side to let the chariots and their scythes run through. But once they were deep enough, the horses found themselves facing a pike wall. Meanwhile the heavy infantry closed in from the sides and behind, to take out the charioteer. No more super weapon.