It is useful in conditions in which you may need many tools, and the demand for inventory space outweighs the need for"high level" individual tools. Two examples that spring to mind are Hunting and the Abyss. In case you need a hatchet to help put up your snare, like for drawbacks. And you can also use it as a tinderbox so that you can cook the meat you get while waiting for your traps to snare.
Who does pitfall hunting for any reason whatsoever? Cooking the meat really is a waste of time, you are better off alching or something in case you need to wait. Cooking the meat can be somewhat useful as you will be idly getting cooking experience while waiting for your traps. You have the option to alch as well. It's personal preference on which one you'd do, but if you decide to cook, then the Dwarven Army Axe can come in handy.
I really don't see what sort of debate you are trying to present along with your line on pitfall searching. One has a variety of choices in regards to training Hunter, and pitfall searching is just one of those choices. It would be very naive to presume that nobody in any way uses pitfall hunting. I was simply saying one instance where the Dwarven Army Axe might be used. I concur that there are other training options which may be more efficient, however, the Dwarven Army Axe can help.
I took the axe with me today to miscellania to block a few trees, I was using it to earn tele tabs and get myself a few strange stones. Its useful for whatever folks want to use it to get. Runescape is a game, its supposed to be entertaining, who can you judge wether the way that people send their time is moot? SecondedI used it today for my strange rocks, I used it for runecrafting, firemaking, woodcutting and mining stones (then I realised it had been only steel : ), on top of using it to get Miscellania.