A few thoughts on the topic.
- We don't really know for sure what they did after the initial clash in most battles. It's usually not the kind of things that the ancient authors, aristocrats most of them, really cared to talk about. So maybe they did try to take on the flanks or rear of the phalanx, but we just don't know about it.
- Human nature: a successful force (whether skirmishers or line troops) might feel like they had done their part and go for the path of least resistance and pursue the enemy rather than join the battle once again and risk death and all.
- Quite simply, their horses might be blown or they might be out of javelins or simply lost in the dust of the battlefield.
- Lack of modern C2I systems. It's not like a trooper in any unit type can easily know where to rally and what to do. So pursuing the enemy and possible looting their camp would have been the default setting of any troop type on the battlefield except the most disciplined and best led.
- Tactic wise: preventing the enemy light troops from joining the fight once again is pretty useful already. If those troops were to rally and appear again on the battlefield, they could be mistaken for the vanguard of a whole new army.
- Lack of impact on line troops: there is only so much damage light troops can do to line units anyway. A commander would probably want to keep the light troops fresh enough for the pursuit or to cover his retreat rather than waste their energy on line units.
- light troops seem to have often been of dubious quality for all kind of social and technological reasons. Afterall the typical ancient warrior was an aristocrat or at least a small landowner. It would be hard for most ancient societies to get the 2nd class citizens/residents/slaves/etc interested in what was mostly a rich people business.
- and then, there are quite a few example of fairly high quality light troops rallying and having a significant impact on the outcome. I'm thinking about the Numidian cavalry at Cannae and Zama, the Pergamese troops at Magnesia maybe, the camp servants and the likes under Marius at one of the 2 battles against the Germanic tribes, a couple of battles of the Peloponesian war also featured light cavalry making a decisive appearance on the rear of the enemy. I'm sure there are more examples.
- Also, some battle descriptions makes feel like some light troops were integrated with line troops and would fight with them against the enemy's main line. Some of Alexander's skirmishers at Gaugameles seemed to have been deployed with the phalanx to help it deal with the Persian chariots for instance. At Magnesia on the Seleucid side, some light troops were with the elephants in the intervals between the 16 regiments of the phalanx.
But really, there n°1 role would have been merely preventing the enemy skirmishers from messing the order of the line troops. Everything else must have been bonus.
One last thing, their is also the issue of defining what light armed forces were back then. Are we talking about skirmishers or simply lightly armored troops ?
Hope those few thoughts helped.
Edit: the battle of Delium (424 BC so a bit before the Hellenistic period) is an interesting case. The Thebans shifted cavalry from their victorious right wing to support their left wing that was in trouble. Also, Plato has an interesting story about the interaction between light and heavy troops during a root:
Quote:"Furthermore, men, it was worthwhile to behold Socrates when the army retreated in flight from Delium; for I happened to be there on horseback and he was a hoplite. The soldiers were then in rout, and while he and Laches were retreating together, I came upon them by chance. And as soon as I saw them, I at once urged the two of them to take heart, and I said I would not leave them behind. I had an even finer opportunity to observe Socrates there than I had had at Potidaea, for I was less in fear because I was on horseback. First of all, how much more sensible he was than Laches; and secondly, it was my opinion, Aristophanes (and this point is yours); that walking there just as he does here in Athens, 'stalking like a pelican, his eyes darting from side to side,' quietly on the lookout for friends and foes, he made it plain to everyone even at a great distance that if one touches this real man, he will defend himself vigorously. Consequently, he went away safely, both he and his comrade; for when you behave in war as he did, then they just about do not even touch you; instead they pursue those who turn in headlong flight." (Plato, Symposium, 220d–221c)
From the wiki entry on Delium
Timothee.