I think I'm bored, so I'll have a go at this.
I agree! I'm kinda slow sometimes so enlighten me on the usefulness of the "cat stance". Then explain how launching punches from the hip is the way to go. Then let me know how wide, deep stances are good. Then show me the error of my ways by explaining how doing all of those things in a pre set pattern for years will in anyway transfer to a real life violent encounter. Yeah, that'll teach me a lesson!
Cat stance is used for a variety of reasons, including gaining an understanding and skill in shifting body weight for evasive action, as a set up for a lead-leg kick, a way to avoid a sweep, and more. If you missed this, go back to class.
Punching from the hip is done to generate power using the mechanics of Karate (body weight through transference with the hips), and it is trained so that you can generate the power source through smaller actions (not punching from the hips). But in order to generate the power from a smaller action, you need to generate it properly from a bigger (more "traditional" action) first. Otherwise you'll never get the power that Karate can offer. If you missed this, go back to class.
Wide stances teach stability, get proper foot position, allow for complete transference of body power through action, and condition the legs for strength and endurance. Once such aspects as these are internalised, the application of them is made more compact and "usable". If you missed this, go back to class.
The concept of a pre-set pattern of movements (kata) is not that "this is exactly how it'll go down", they are a teaching method designed to give you the strategies and tactics of the art in question in such a way that there is no aspect of "individual personality" getting in the way and corrupting the approach from the proven methods. By training it properly (repeated methods with accurate visualisations of the applications and attacks they are designed against) you are "teaching" your unconscious that this skill is powerful, and useful, meaning that when needed, it is there for you to use. It is not trained in a vacuum, and is not the only method used. If you think it is.... you know what? If you class your art as "Real world", and post the way you have been here, I don't think you have the first clue about martial arts at all. I don't think you'd get much out of them, as you have no idea what they are, how they work, what they do, why they do it, and so on. Bear in mind that I am not saying anything about fighting or violence here, just martial arts. And you seem to be making the classic mistake of thinking the two are the same thing.
That move wouldn't work on a resisting opponent in a thousand years!
Really, it has worked on resisting opponents for a thousand years, actually... it's a standard movement in many Japanese systems (known as Oni Kudaki in my arts, also found in Aikido, and many other arts), and is found in wrestling as well as many other forms (I think you were advising wrestling at one point, yes?). There are forms of it in BJJ, and MMA. So, uh, wanna re-think that last statement?