Actually...
While I don't agree with the original post's method of doing it, I think it might make sense to have different sword techniques or martial arts schools or whatever. These would generally be represented by bonuses and disadvantages to certain purely physical actions that people could perform anyway (a quick cut to the legs, a stab to the eyes) -- they could then have 'special techniques' that would be be 'macros' for a combo of attacks, often, which the practitioners of that technique specifically train in so they can pull them off faster and more effectively. (Although, I suppose once magic is added their might also be supernatural combat techniques as well.)
But the important part is, this would allow people to specifically train in those purely physical techniques. Right now you can only train in 'sword' or 'wrestling' or whatever -- which is absurdly general. Instead, you could train in a specific sword stance based around parrying every attack, or in a wrestling technique focused on takedowns, or whatever, so different swordsmen or whatever would have different specialties. Some fighting techniques would be better against certain kinds of opponents.
Of course these would be randomly generated and based on culture. So you could have the Giant-Slaying Stance from the far north, which helps against larger creatures.