There have been a lot of good points made about stances in general in the preceding. They speak to the implicit assumption in the OP that a stance is some kind of physical configuration you assume and then horse yourself around in for the duration of the fight, setting up the obvious straw man response that `and of course, no one actually fights like that!' But stances, in the sense that the OP seems to be assuming, just sketched, do not exist in the kata-based sources of TMAs. They came into being as Bill Burgar notes in his book on bunkai for Gojushiho
Five Years, One Kata, only when kata training was replaced in preward Japan by kihon line drills as the method of choice for large-class instruction. Chaps like Itsou, Arikaki, Azato and other founders of modern karate taught one- or two-on-one, and emphasized kata as the method of technique development. And in the kata, what we call a stance was nothing more than a momentary conformation of the body in order to
project body weight into a technique. As Abernethy notes in his chapter on `The purpose of stances',
In combat, the stances are used in one of two ways. The first way that stances are used in combat is to ensure the correct distribution of body weight. The use of body weiht is critical if your techniques are to be successful, as all techniques should be applied using the entire body. The second way that stance can be used in combat is in the use of the physical position of the legs themselves. In this instance, the legs can be used to physically controll the opponent.
And he goes on to add a caveat that could have been aimed directly at the OP itself:
The word `stance has connotations of something fixed and immobile. In combat, however, situations are constantly changing and hence the stance should also be constantly changing. The distribution of the body weight should not be fixed, but should b constantly changing depending on the technique being employed at that time. Stances will be assumed as and when required, before instantly shifting the body weight to the next appropriate position.
(p. 203). There's a nice simple example which makes the point fairly clearly, I think. Take Shotokan's Taikyoku Shodan, which was adopted whole into KKW TKD's Kicho Il Jang (for some reason the KKW overlooked purging it, in spite of its Okinawan/Japanese sources.
Someone was sleeping on the job...

). I interpret the initial kata sequence
(i) ready position, preparatory to a 90º turn into a left front stance/down block;
(ii) 90º turn into a left front stance/down block with chambering retraction of the right fist;
(iii) movement into right front stance/middle lunge punch with chambering retraction of the left fist...
as a `minimal combat sequence', with attacker and defender starting off face-to-face and the attack initated by a righthand wrist grab by the attacker, to the defender's right wrist, arm or shirtfront, and the corresponding response (where in general combat move (n)' is the oyo for kata movement (n)):
(i)' the defender covers the attacker's wrist with his own right fist, or reverses the wrist grab—this is one of the very earliest SD techs we teach them—and in either case, simultaneously (a) twists the captured wrist counterclockwise, and (b) turns quickly clockwise pulling on the wrist—this is the concealed meaning of the apparent presentation of the defender's left side to the the attacker at the outside of the form (something that would be suicidal to do in a street confrontation, obviously)...
(ii)' followed by simultaneously (c) driving the left forearm against the attacker's now forcibly extended right arm just above the elbow (the lower part of the `chambering' phase of the `down block'), (d) hikite of the trapped fist by the defender's `chamberinging retraction' of the right fist (pulling the attackers right fist into a maximally extended positon to give the defender's arm pin on the attacker maximum leverage and trapping the attacker in position)
and projection of the defender's full body weight forward into the pin via the `front-stance movement', forcibly driving the attacker's upper body down and exposing their lowered head to the defender's upcoming counterattack.
Having driven the attacker into a lowered position via the arm pin described, the defender (e) quickly moves the left arm from its pinning position to near the defender's right ear and lowers it in hammerfist strike or knifehand to major targets on the attacker's head: the carotid sinus or larynx. The downcoming strike can be subdivided at the defender's discretion into (e1) a spearhand elbow strike to the attacker's face (eyes are a good target) and (e2) the payoff hand strike to the selected target.
(iii)' A smooth muchimi shift of the striking left hand to a grab on the attacker's ear/hair/collar is immediately followed by a simultaneous (f)hikite retraction of the left fist to pull the injured attacker in and around and (g) a right-hand strike (maybe a fist, but I think a palm-heel strike is sounder) to the attacker's face with the full weight of the defender's body moving into a right front stance.
This is a pretty harsh, effective response, no?—especially considering that this is the first, most elementary kata you learn in Shotokan and the first hyung you learn in Song Moo Kwan TKD. But notice that it hinges crucially on driving the full force of the defender's bodyweight into the attacker's hyperextended arm. I've been both uke and tori for this oyo and believe me, no matter how noncompliant a mood you're in, you will
punished if you try to fight the arm lock when it's executed by a halfway competent technician. But the weight projection is crucial. Picture it: you've extended the attacker's arm while pinning and twisting his wrist, you've established a fulcrum just above his elbow, and now you drive all your bodyweight into the pin by moving the leg on the other side from your trapping hand forward, driving your forearm forward and
down. Film that move and 100 MAists out of 100 will identify it as a left-leg front stance. You only stay in it long enough to set up the elbow and throat strikes I've mentioned, then you immediately come forward on your other leg to bring yourself into range to deliver the followup hard strike to the jaw (or maybe temple). And that movement looks exactly like a standard right-leg front stance kihon movement.
The OPer brings up the cat stance, and asks somewhat incredulously if anyone ever uses a cat stance in a fight. Without going into the literally gory detail, consider what Abernethy says about what cat stances really are (to see exactly what he's talking about, you need to see the photo sequences which accompany the description):
Short cat stance
The opponent has been thrown to the floor in such a way that you still have control over one of their arms. Push your foot up against the opponent's back, lift your heel and assume short cat stance. Pull the opponent's arm back over your thigh in order to hyper-extend their elbow joint (Figure 7). You'll notice how the physical position of short cat stance is used to control the opponent and to provide a fulcrum for the arm lock.
Short cat stance projects the body weight backwards and downwards at a fairly sharp angle. One technique that requires such a distribution of body weight is the following wrist lock. The opponent has seized your wrist (Figure 8). Pin the opponent's hand with your free hand whilst quickly rotating the arms. Then cut against the opponent's wrist as your hands move towards their body (Figure 9). Grab the opponent's forearm and pull your hands down and towards you. Assume short cat stance at the same time in order to project your body weight in the same direction as the hand movement (Figure 10). This will lock the opponent's wrist and for the opponent to their knees. If you try to apply the lock with the arms alone, the opponent should be able to resist the pull. However, by dropping the body weight into short cat stance, the effect of the pull is greatly multiplied.
(pp.205-207).
That's the sort of thing that the cat stance is used for—imposing unacceptable pressure on a joint you've used the kata `instructions' to pin. Likewise, Abernethy shows how long cat stance is applicable to disrupt an attack from behind, how the back stance sets up a pivot point to use in throwing the opponent... nothing remotely like the assumptions that the OPer's initial and subsequent posts seem to incorporate.
It was only when techniques were detached from the flowing subsequences of the kata and turned into separate, stand-alone moves in a strategic and tactical vacuum that stances were reified, no longer the mere transient by-products of combat moves but instead...
things on their own, things to practice and hold. They
never had that status in the formative days of karate, when kata, each incorporating several whole combat-effective subsequences, were the core curriculum—yet another case where history turns out to shed an invaluable light on seemingly confusing technical matters.