With Melee you can kill animals while running on a rampage, even with only 10 Melee Combat
Unless you're going to build someone to death I don't think it's going to do much in a fight.
Doesn't answer my question. Can you punch a tree into a chair?
In a larger society or even a village, Carpenters would have no business fighting because they would be busily working away in their stores or being escorted to a forest to get wood.
Not everyone has to waste skill points in combat so everyone in your village has top-notch fighting skills but the artisans lack the ability to create high quality works because they wasted it in a skill tree they really shouldn't need as artisans.
That's what soldiers and guards are for.