So what would make an axe versatile, or good for wide ranging use? Maybe first it should be understood how wide ranging use is defined. It would be a mistake to include things that an axe has no busisness being used for like pounding with the poll, hardened or not, though it's a common enough misuse even by people with experience, so certain actions can be eliminated also to include digging, though chopping roots is legitimate. Then going on to a universal use all the specialty axes can be eliminated, mauls, side axes, twybills, the range of carpentry axes. As far as activities carried out using an axe there are the conventional uses which first spring to mind to include splitting firewood, maybe chopping down trees though it seems hard to justify in any way other than play, but play is always legitimate, same with bucking or most perpendicular to the grain actions, limbing, (a perpendicular to the grain action), what more? All of these have a particular context in common that could be called field work maybe. But then there is the other category of activity, done typically more close to home or workplace, more often than not relating to building and carpentry, maintenance and domestic work or even craft work so, preparation work in carving, and building materials, making kindling, fencing, chopping ice, slaughtering animals, splitting and riving longer pieces of wood. I don't think any of these are too remote and so should be included when considering versatility. So then the physical characteristics that make an axe useful in such a range include, in the middle or towards the small side in terms of size, with a handle length not long but maybe longer than the head size may suggest, the cheeks would be rather thick providing for a gouging action which requires not so much skill, with a related rounded bevel and a fair arch to the cutting edge. Also a form that allows a grip up high and in behind the cutting edge for controlled chopping and pairing. I guess it's clear now that I'm just using words to describe the picture up there.
E.DB.