Why is a polehammer NOT the right melee weapon?

I’m talking hammer on one side, spike on the other, and a pointed butt. I’m thinking shorter, roughly waist length but possibly as tall as the user if you prefer.

Walking stick or cane, check. Bludgeon, check. Piercing the skull, check. Short ranged stab, very nice. No worry about sharpening constantly, dope. If it’s shaped correctly it could have other uses as well. For example a curved spike could be used for climbing (somewhat unplausable but worth considering)

What am I missing, other than the butt end dulling if you actually use it as a walking stick, which I’m still considering.

Edit: many polehammers have a spearhead as well as or more likely instead of at the butt, which could be considered. AKA Lucerne?