Unlike most infantry archers, they wear a decent set of armour. That means they also don't die nearly as readily when someone throws stuff back at them. Way back in a few Hayasdan campaigns I learned right fast the buggers are not something you want to have a firefight with if all your guys have protecting their hides is shirts.

Even if your guys are on horseback. You're likely to run out of ammo before inflicting meaningful casualties on the Syrians unless you have something like three to one advantage - and that had better feature slingers.

Personally, I found that once the AS started adding these guys into its stack parade mopping them up became a lot harder, and tended to revolve around using the Hai Bodyguard Terminators to hunt down the Syrians from amongst the other troops at the very beginning. Not fun.