Generally (and it seems the case here too) the difference in types are simply resistances from enemies.
With a 0 resistance foe, nothing going.
However add resistances (and there are seperate ones for piercing, slashing and crushing as a certain spell told me and should actually display in the inventory :/) and you're starting to get a whole other story.
Makes sense to me skeletons and arrows don't quite match

Personally I would think the best solution would be some skills that do alternative damage. So you'd still mostly do piercing, but if you want otherwise you aren't exclusively tied to special arrows.