So it seemed that from the accounts of Thermopelea, Roman military strategy of waiting out an arrow storm, and Knights holding out for hours behind a shield wall during the first crusade it suggests that arrows were not effective weapons until later on, however it seems that archers and skirmishers were a staple part of armies early on in Greece, why?
They were fairly to reasonably effective. Otherwise nobody would have bothered with them in the first place. War is not about having the biggest baddest whatever. It is about applying force in the best possible way.
Light infantry were good or important enough to always have some in your army. And they were cheap, or at least cheaper then heavy infantry. A light infantryman had much less armor and needed less training to be reasonably effective. Often the poorer soldiers were found in light infantry units.
One job of the light infantry was scouting. Look for the enemy, observe them, go back and tell your commander about them. While you at it, you can - if the opportunity present itself - lob a few stones or arrows into the enemy.
Another job is to make sure the enemy cannot do whatever it wants, that's skirmishing. The enemy's heavy infantry has to form up first and keep in formation after that. Light infantry can make that difficult. Their harassment of the enemy can delay the formation they want to achieve, kill a few troops, and postpone his advancement somewhat.
At the same time, while you are in front shielding your own formation you prevent your enemy light infantry colleagues to do unto you what you want to do to them: deny them scouting opportunities, and harass your own troops.
It isn't the job of light infantry to stand and die on the spot. That's the work of the triarii, or more general: the heavy infantry. As soon as the enemy starts advancing, or gets angry enough to charge those pesky light infantrymen they run away. Nothing wrong or dishonorable, it's part of their job. The light infantry moves through their own lines and reforms to do something else. Like harassing on the flanks.
Heavy infantry is there to stand and die if necessary. Light infantry is there to bother the enemy and live to fight another day.
Another job the light infantry did was pursuing the defeated enemy. They are light, remember? Meaning: carrying less equipment, thus can run faster. The enemy has to drop as much as they dared, which is pretty much everything. If they want to fight - and most won't - they will have to turn around and face your light infantry. That puts them at a huge disadvantage.
Most casualties didn't happen during the battle, but afterwards. That was a real important job for which light infantry was ideally suited.
As this is as general as can be (the time period is huge) I put together just about everything that is not heavy infantry, for simplicity sake. It takes years of training to become a really professional archer and more years to become a proficient slinger.
Archers were valuable during the Medieval period, at battles like Crecy. That's because they were then "formation" troops that made up the backbone of the English army at Crecy (and perhaps one-fifth of the troops fighting on the French side were Genovese bowmen. The Mongols also used archers (on horses) with great effect.
Archers were less valuable during Greek and Roman times. They were NOT formation troops (the latter consisted of armored men in phalanxes or legions with spears or swords). Archers, slingers, etc. were "skirmishers for "prebattle," (ambushes, probing attacks), and post battle (pursuit) maneuvers. Unlike medieval archers, they did not constitute the "main force" during the heart of battles.