You wrote: "So it is skewering for me."

You are very wise!

Did you know R. J. Secor lost his ice axe during an accident, as he glissaded down Mount Baldy? With no way to self-arrest, he suffered major injuries; the accident put an end to his climbing career.

An ice axe is a serious tool, and, like many tools, it can be mishandled to the detriment of the user. Yvon Chouinard, in "Climbing Ice" stressed that, when used as a walking stick, the pick of the axe should always be aimed forward (in the direction you are moving). Otherwise, if you stumbled and fell on the thing "it could interfere with your digestion."