Warning: These are my own thoughts, not necessarily YKM.
Stances - the word conjures up images of old-time, classical kung fu training. Holding the horse stance until the incense stick burns out. Or movie images of the Shaolin Temple monks, holding glasses of water on their heads, forearms and thighs until the weaker ones collapse in a wet pile.
All valid, but what is the point of stance training? It is a subject belittled by the MMA crowd as having nothing to do with fighting, and other fitness professionals who would rather have a person do thousands of body weight squats (on a Bosu ball, no less).
My opinion is this - static stance training develops the muscles in a sport specific way. Also works on the character, chi development, body awareness, and other areas of peripheral influence on fighting/combat. It is part and parcel of training the complete person. It is not the be all/end all of training - merely a part of learning how to move.
I posit that by learning to stand in a deep, steady horse (or other stance) - you are learning to root (albeit unconsciously). As you progress in training, you learn to do this in whatever position you happen to be in (i.e. a one legged position, a narrow stance while standing on a crowded train, etc.).
In my opinion, stances are to be used to impart force/power into the adversaries body by having proper structure, to not rebound off your own strike, and to avoid becoming unbalanced. They are also meant to be used to move your body in a controlled manner (e.g. to spin and unbalance a foe) - moving from one position of strength (or "stance") to another.
Also, culturally, there may have been less free time for training in the past, so cultures developed multi-faceted training exercises, rather than isolating muscle movements - not lifting weights every day, 45 mins of cardio 4 times a week, and then fitting in a 2 hour boxing workout.