I will assume that every person reading this has experienced the benefits of stancework. Each person has realized that great effort foreward, such as pushing a vehicle, uses the bow stance and the stability to support anything, such as lifting, uses the horse stance.
Also, many of you may be tired of the standard tournament tactic of "frontal assault or run away". You may notice that the military tries to secure an advance by creating a safe zone for their own uses. Fortifications, no matter how tenuous, are also important. Personal combat is not different from this. Tactics which consist of running into range and then running away do not win battles. Any body who watches the History Channel may notice how the Romans put a stop to this. Even the Germans with their "charge down the center" tactic still avoided fortifications whenever possible. The German tactic is, more precisely, "charge down the center of their weakness". An understanding of stability, how to maintain and exploit it, is a cornerstone of all types of combat.
In most Martial Arts, Stancework is the beginning of this training. It is the first step to controlling the opponents capacity to attack. Advancing while maintaining the stance is what you do, at a simple level, when the opponent is confused. They say that they are looking for a weekness but, their tactic of menial strikes in the hope that you will stray from your stance out of frustration, they simply hope that you will make a mistake. These fights can go on for quite a while as they "score" inconsequential hits with which to salve their Ego. The bouncing around is simply an anxiety reducing habit they have developed.
Mohammad Ali used to switch quickly from stance to stance while moving. However, he was never in a position where he could not hit with power. Ali was quickly moving from a position of power to another position of power. Others simply hop and pretend they are receiving the same benefit that Ali had achieved. Any Boxing match should illustrate the dangers of being in the air when the opponent attacks and the weakness of your own airborne attack.
The Side Horse Stance is defensive at the basic level. This posture is designed to withstand a frontal attack and allow you to attack with both hands equally. The stance itself allows you to follow an encircling opponent by simply turning at the waist. The opponent has to run a circle at least two steps in one direction and seven or more in the other direction just to be in a position where both hands cannot reach. This is a lot of work for the attacker. While it is true, and obvious, that an overwhelming attack will nullify the benefits, I challenge you to find any defense to an overwhelming attack. Even running away can be nullified by an overwhelming attack.
The bow stance has the quality of focusing power in the direction of advancement. Is is convenient to advance this way when you know that the defenses of the opponent can be breached. While many people discuss the limitations of stance. They ignore how those weaknesses are minimized through movement. The primary weakness of the bow stance is to not be able to reach the opponent.