You took it incorrectly. You opinion of maces is strictly Europocentric, more of it, late-medieval Europocentic, while we have steppe, half-steppe and desert cultures in the game. The sabers, maces and flails were there hundreds of years, if not a millennium before, because of developed horsemanship. When Vikings went to the shield wall on their own, steppe people were warring on the horses of theirs. Mace was better than axe for horseman because it did not stick, chance to leave it in the opponent body or armor was minimal, especially with added velocity of horse. And of course, axes never meant to
cut, they are cleaving devices, designed for penetration. Isn't it obvious? Will you chop the tree in the same move pattern as you are cutting loaf of bread?
In our history both axes and maces weighted roughly the same 1-3 kilos. When armor went high, both weapons seconded. But there were some borders. Velocity matters the same as weight for impulse, but excessive increasing of weight severely limited ability to accelerate, along with just handling. Moving further, the completely blunt maces got flanges. Ask yourself why was there a need to put dull blades (still blades though) to the head?
As for me, that pointy part is just like axe's toe or heel, eh?
There will be still no variety, because the whole model of yours ignores the fact that
any hard object will deliver energy. And this energy will not dissipated to somewhere, but will be spent, firstly, to the armor damage and secondly to the body behind with blunt trauma if armor was not perforated or pierced/slit wound if it was. Funny thing, most people are agree with an axe as good shield breaker, but hey, it's marked as cut, I should have no damage from it.
I only wanted to say that any model with zero damage will not be unrealistic, but just silly, because IRL first we have blunt force applied, then penetrating ability, then, if in place, cutting damage. In your scheme you are implying that axe has no weight and can't perforate thing, and therefore it shouldn't damage armored unit at all, while real damage received should be laying somewhere between blunt and pierced.