Actually, the reason slingers are still prevalent in the period is precisely due to the fact that archery is still relatively under developed. Most padded jackets, leather armour, linothorax and scale armour were very effective in protecting the body from arrows. Even chain-mail has decent stopping power because of the padding worn underneath. If you want to hurt armour units, slingers and javelins (another prevalent weaponry) are your answer.

However, I'm not saying archers are useless. Cretikoi, Syrians, Steppe and Caucasian archers can do pretty decent damage- more so if you shoot people on their (unshielded) backs. Nonetheless, you'll get more dividends using the archers in their historical role: harassers, ranged flankers and warding off un-armoured (light) troops. They work wonders in slaughtering those pesky skirmishers, evil axe/rhomphia bearing killers and Gaesatae (shoot their unshielded flanks).

As a steppe player, empty your quivers on the enemy ranged and light troops first. Their armoured men will wear themselves out running after your horses. Phalanxes can be shot on the back and lots will die. Even if they're heavily armoured, once you've killed off the light troops guarding their flanks they are notoriously vulnerable to a thunderous charge to the flanks and back.