You are all somewhat correct. Of course that means the inverse is true too. If you want a good stick in solid water ice then nothing will beat a modern tool with a curved shaft and heavily drooped pick. If you want to dry tool (hooking roots in the hiking context) then a pick meant for that will be optimal. I you want to use if for security on steep snow then a long straight shaft will be best. If you were a carpenter and could pick one hammer what would it be? Framing? Finishing?
So what's the answer? Like many things - it depends. The traditional mountaineering ax will be the most versatile - may not be ideal for all applications but "good enough" when accompanied with the right technique (45 years ago I soloed Pinnacle Gully with 2 straight shafted axes. Today I'd want the fanciest tools I could get)..
Actually for the OP's use case I think there is a good argument to be made for having a good modern tool - doesn't have to be top end - could buy one used at the IME consignment shop or where ever. But only deploy it when encountering (relatively) steep ice.
So what's the answer? Like many things - it depends. The traditional mountaineering ax will be the most versatile - may not be ideal for all applications but "good enough" when accompanied with the right technique (45 years ago I soloed Pinnacle Gully with 2 straight shafted axes. Today I'd want the fanciest tools I could get)..
Actually for the OP's use case I think there is a good argument to be made for having a good modern tool - doesn't have to be top end - could buy one used at the IME consignment shop or where ever. But only deploy it when encountering (relatively) steep ice.