The point attack on axes is supposed to represent (in my opinion) using the lowest point of the sharpened edge in a kind of downward pull or hooking motion, rather than a straight chop (an edged attack) or hammer-blow with the back of the blade loop (blunt). It should do much less damage than it currently does, but it seems to work as well on legs attacking as blunt defensive counter-attacks from spears, suggesting a kind of acknowledgement of the entangling properties of these particular targets, weapon aspects, and situations, which doesn't necessarily need to be changed in and of itself. Hand-axe and woodsman axes are the only ones other than the battle axe that deserve decent combat ratings, as these two are built for utility and ease of use, and strength and durability, respectively. The battle axe has no utility whatsoever, it's utility is reflected in its attack bonus, its strength is reflected by its excellent edge damage, and its durability is shown in its ability to deal decent blunt damage, which I imagine is simply using a purpose-built weapon in a less technical way to pierce armor more efficiently.
The various body parts of humans and animals being more or less effected by different weapon types can be explained away by base armor values for animals bodies'/their particular skins' strong and weak points, and weak overall armor coverage on humans, both of which seem realistic.
Overall, I like the OP's suggestion though, shortswords are only viable if your sword skill is your best weapon skill, which would be silly of you.