Hmm! Strong opinions. Well, I've only played with an ice axe briefly, so this is mostly hypothetical -- my 2c.

But I can see some summer utility in certain situations. I often walk on trails where invasive, very spiny plant species are an ongoing problem. I have wished more than once for a long-handled digging tool to thin out the herd as I'm passing through. A shovel is too heavy to schlep along; a thin, strong pick on a walking stick would fit the bill.

To quote a movie that (purportedly) quotes a famous American: "I don't care what anything was designed to do, I care about what it can do."