I'm guessing that the devs wanted to ground he weaponry in our reality, and apparently axes like the one in your avatar were never a thing in combat. Double-bitted axe were either ceremonial (in Greece) or forestry tools.
Speaking about RL your exception is ok: of course Axe of my avatar is a fantasy representation (or maybe only cerimonial weapon) but in the past Axes were often used in melee battles. Not commons as sword of course, but, anyway, they were used.
That said we are speaking about fantasy game: imho POE is wery well designed but considering that combat is main of gameplay, a little more items (also with artistical representation) will be nice.
Bye
Phant