As a long time mountain guide and mountaineering professional, I own a handful of ice axes and self arrest tools like the BD Whippet. Personally, I just don't see the use, or rather the benefits outweighing the costs, of taking of taking a longer, heavier ice axe on a mountain hunt. In some of the earlier threads on this topic, a few folks have offered a number tasks that you can use a mtn axe for in the context of a mtn hunt. I'd submit that many of these tasks can be accomplished just as well by a smaller, lighter tool, or that they aren't really crucial tasks to be able to perform but rather something one might use a tool for because they had the tool. Removing rocks from your tent spot for example.
That having been said, I've taken a small, lightweight axe on a few goat and sheep hunts, though I have yet to use one for climbing or self-arrest. In my experience, trekking poles are far more efficient for the vast majority of the terrain one will encounter on these types of hunts. If you have chosen well, they are also significantly lighter than a long ice axe. Carbon fiber poles are light and extremely durable. They are also a lot quieter when scraping along in the rocks and talus.
For the sake of speaking the same language, I define a "long" axe as one that is longer than 70cm. For most average height dudes 5'10" to 6'2"-ish, an axe 70cm or shorter won't be useful as a "walking stick" until you are on 30+ degree terrain.
Again speaking personally, I can't think of any niche application that would make a long heavy axe worth taking, even on a trip where I may not have to carry it for 50-100 miles. Most of my mountain hunts involve lots of up and down and long mileage days and so I tend to be very picky with what I choose to carry along for the ride. I put a lot of emphasis on versatility and need vs. want.
When heading into goat or sheep country, I typically find myself choosing between the following options:
1) trekking poles only,
2) one whippet and a trekking pole, or
3) trekking poles and a small, light axe
I go with trekking poles only when I don't expect to have to cross any snow or ice with consequential runouts or hazards I could slide into.
I go with the pole + whippet when I might expect to cross a short but steep snow or ice patch or two, or perhaps traverse a low angle glacier. I also have a 35cm ultralight axe that I cut down I'll bring along for certain types of missions as well, again typically longer traverses of low angle terrain where I want a self arrest tool, but may not want to deal with a whippet for the duration of the trip.
I'll go for the more functional climbing sized axe (65-70cm) and crampons when I might expect to find myself climbing on or traversing longer, steeper (30+ degrees) sections of now and/or glacier ice above consequential terrain.
No hard feelings towards those that like to lug the long stick along and I totally get it. If you have become comfortable with that tool as part of your mountain kit, more power to ya. Personally I find them heavy, unwieldy, noisy, and less suited for a number of tasks as compared to other small, lighter tools. First and foremost ice axes are snow and ice climbing tools, and self arrest tools. A longer axe actually makes both of these applications, climbing and self-arresting, quite a bit more difficult if not dangerous as compared to the more common sizes used in mountaineering.
In my experience thus far, there just isn't that much steep snow and ice climbing "typical" goat and sheep hunts. Can you seek it out. Of course, and going into difficult terrain where others can't, won't or shouldn't can be good strategy if you have the skills to do so safely. Winter in places like Kodiak or SE are certainly an exceptions to my "typical" comment and having an axe along for snow, ice, and frozen turf in those conditions would be mandatory in my opinion.
There is long list of very good reasons the "alpenstock" faded from favor in the world of mountaineering many, many years ago. They were functional, even revolutionary in their time, but that was a long time ago.
With regard to brands, lots of companies make a wide range of quality axes and crampons. I am partial to Grivel and Black Diamond for axes and crampons. I tent towards to the lighter but less durable aluminum models for mountain hunts where self arrest (vs climbing) is the larger consideration. I like strap-on aluminum crampons for applications where I would only expect to use them on snow and ice. They dull easily and steel would be a better bet for turf and frozen rocky terrain.
