I don't think going down was a priority. When you are under attack, you want your archers to rush up to the walls, with some extra fighters for good measure, and you don't want them to go down until the enemy has decided to leave. At that point, the speed of your archers going down doesn't matter much.
Hmm...most archers would be right handed and used to holding/carrying their bows in their left hand (during battle at least), which I assume would indeed be easier ascending a clockwise staircase...wonder how you'd test that theory!