While the aesthetics were not the intent of the question to begin with, since so many want to challenge me on it I suppose i'll bite.
The cutting head of an ax (the beveled portion) is NOT designed that way because an ax is a cutting weapon. It is designed that way because that is the most efficient design for a wedge. An ax heads purpose is to focus the force generated by the weight of the head when swung. The thinner the bevel is, the more concentrated the force is. Ever tried to skin an animal with an ax? or even slice some tomatoes? That is because its designed to be a chopping implement, not a cutting one.
Both an ax and a sword are mechanical levers. The difference is that the weight is distributed on opposite sides. The majority of the weight in an average sword is in the handle towards the pommel. That means when you strike a target the force in your swing will be equally applied back against the blade. Since the weight is at the handle its natural response is to compensate at that fulcrum point, allowing you to slash across a target - taking the blade from one corner to the other. Axes have the majority of their weight in the tip. They are designed to push through an intended target, initially for making chopping wood easier. If you strike a target axes are more than likely going to bury themselves into whatever you hit, not slash across it. Since all the weight is at the tip, you are at a severe disadvantage in controlling the forward momentum of the weapon as compared to a sword.
I will still contend that the majority of damage that axes generate are due to their ability to create blunt force trauma not cutting potential. Its more efficient to cut with speed, not weight. Which is why swords have always been preferred for cutting. Its not that axes CAN be used against armor, they became preferred over swords in some cased because of the blunt force trauma they create. The "main" purpose of an ax is to chop - not cut, sever, or slice. Furthermore, a hammer with a 5lb head and an ax with a 5lb head will generate an equal amount of force when swung. The only difference is the surface area that weight is distribute on. Perhaps an ax is not totally a blunt damage weapon, but it is certainly not a slashing one either.


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