Great info. Oddly, in MFOTH, The axe is supposed to be used before crampons. How often do we bring both Micro's and 12- point crampons? If you just bring the Mciro's you should be ready to bail if you get ice that would overwhelm your footwear. (Yet we know some will prevail missing, or mis-using. equipment.)
Only a few mentioned but expect most do here, a leash is mandatory. Axes have been found several hundred feet above their owners lifeless bodies before. Mountaineering axes are probably the proper tool for braking if glissading from Mt. Field on the steeper sections of the Mt. Avalon Trail or for those with butt sleds that descend trails as a fairly decent rate of speed.
My most memorable axe use was with rotton snow in the Carters and not as intended. My snowshoe punctured the surface where it had melted underneath but slid forward to wear it was under a frozen crust I couldn't pull it through. Poking the crust with the pole might have provide results eventually, I took the axe off my pack and made quick work of the problem.