Sorry if this one's been suggested already, I've done some searches but with the sheer number of topics its impossible to check them all. I was thinking that some skills have definite companions, woodchopping and axedwarfship come to mind. Seems ridiculous that a legendary woodcutter is as much a novice when it comes to using the axe as a weapon as novice. Perhaps some sort of 2:1 ratio or something similar would be appropriate? Ie for every two levels of a particular skill you get one level in its complement. Other ones I can think of off the top of my head are blacksmithing and metalsmithing and wood carving and bone carving.
Not sure about this idea in particular, but I know I've talked of (a side-suggestion, at best) a "skill tree" method that might have some tasks use a composite number of mini-skills. (e.g. crafting of wooden bracelets having "material knowledge/wood", and "small items/jewellery", compared with making wooden beds "material knowledge/wood", again, but associated with "large items/furniture", at its simplest, with a possibility to be far more complicated and sub-divided...) I could see this applying to an axe skill (generally being used to the heft of one) and partnering that with either some knowledge of lumberjacking or combat, according to situation.
The argument from some would be that attacking a rather passive tree (slumbering Ents, notwithstanding) with a view to felling it is sufficiently different from using the same axe against a being who is quite probably trying to kill you (and, if not, will actively attempt to avoid your attacks) and may very well possess a weapon, shield and/or armour of their own. Your woodcutter would be unable to make their axe hit anywhere vital if their combat experience was vastly less than their opponent, while the fully armoured axedwarf could be quite inefficient in the opposing role and as likely to jam the axe in the tree (or being felled upon).
I think it's all a matter of balance, and consideration, but probably needs a vast overhaul if practical steps were to be made in that direction, as opposed to sticking with the current style of separation that we're rather used to and works Ok.