While I realize in standard melee, EI are far better than slingers would be, I wonder if the added bonus of missile attack would be enough to field slingers instead of EI. Most of the infantry you will face will be either EI or phalanx. Either would be easy pickings for either slingers or archers.
With Scythia, I tend to field more CAW than Axemen. Granted, CAW's melee attack and defense are far superior to Parthian slingers and archers, but the same strategy is used. I would assume that the difference in attack and defense makes the strategy less effective for Parthia. Something for me to try sometime, I guess.