It's because slingers have the AP attribute, which effectively makes it impossible to just stand there and take it, unless you're in some crazy phalanx mood. And no unit is in such a mood today that I know of.

Also it's vitaly important for your slingers to hit the guys at the right angle: from their right or from their back otherwise the hughe shields will block nearly everything coming their way. Of course you get the best effect by making them run by hitting them once with a single missile volley (preferably slingers with the AP attribute such as the eastern and greek ones) and when they're running (thus when they can't use their shields properly) unleash a rain of arrows/ slingshots. Given the AI this works out especially well if you deploy your missile units behind a single line of phalanx units, or use your slingers to soften a garrison during assault. A bit of an exploit but hey, this one isn't even that ahistorical: slinger were notorious for breaking whole armies by simply provoking a couple of units too much.