How does a shield counter HA? All HA has to do is avoid him, bump him when he's distracted, charge him head on with arrow nocked so he either gets shot or bumped, circle around and crossfire with other ranged, etc. There's a ton of choices for the HA and none for the shielder, beyond a lucky hit if the HA is retarded enough to hang around in his small melee range.
1 vs 1 is a useless comparison anyways, it only happens rarely at the end of a round. In a team vs team setting HA simply has all the best tactical options open to it in every single instance (barring siege like maps where mobility is restricted, and even then they can hang behind the inf blob, pacing back and forth while shooting at the enemy inf blob and other ranged beyond, from a much better angle than other ranged who have to look for shots in between inf and inevitably tw). As someone said, there's a reason Khergit were/are unnoficially verbotten in every native battle server.