I'm quite sure this magically balancing hatchet(same thing happens to the old axe if you put it in a certain way) is supposed to be more of a thing for looks. All the hatchets that are not being wielded by zombies are sticking out of a piece of wood or something. Makes it look better I suppose if the the hatchet is sticking out of the wood.
Good theory but I'm not sure myself. When you find a hatchet stuck in a chopping block, the handle is up in the air so only the blade is touching anything. However, when you drop the hatchet on the ground, both the blade and the handle touch the ground. This difference in behavior implies that when the hatchet is stuck in the chopping block, there's some sort of "lock" on physics that prevents gravity from affecting the handle, and thsi "lock" doesn't happen on the ground. It seems logical to assume that this same "locking" mechanism would also keep the whole hatchet on edge on the block without needing anything funky in the hatchet itself.
The behavior of the hatchet on the ground, where gravity alone should be affecting it, seems to me to be as shown in the sketch below:
In this theory, the hatchet's center of mass is well out in front of the edge of the blade, and also outside the bounding box of the hatchet itself. Thus, when you drop the hatchet, it spawns in your "hand" in a default orientation, which would have it lie flat on the ground. But when you release it, gravity/physics starts to act on it. Because the center of mass is outside the bounding box, gravity can pull it down through the floor. Meanwhile, the bounding box prevents the hatchet itself from going through the floor, and causes it to rotate into a vertical orientation along the axis defined by the hatchet's 2 points of contact with the ground.
If this is what's actually happening, it has implications for using the hatchet as a weapon. I'm sure that in the game, the location of the center of mass is very important to the physics of swinging and hitting with a weapon, just as in real life. So if the hatchet's center of mass is in an unrealistic position, it would give unrealistic results in combat.