The applications for trekking poles and ice axes in my opinion are quite different with the ice axe being a very specialized piece of equipment required mostly in extreme alpine/high elevation environments. An ice axe is a tool that is a bit more applicable in situations where ice, glacier crossings, extremely steep/slick rock, or self-arrest potential are likely. The trekking pole on the other hand is more of a mobility tool where steep and uneven terrain, long mileage and heavy loads are likely to be encountered. Having said that, there are some instances where an ice axe can be used instead of trekking pole(s) but those in my experience are few and far between. They are two different tools for two different jobs. Now before someone gets offend and flames me, I've used both extensively so I'm qualified to make the observations I'm making having used both over many years.
