We are on the same page. I never thought anyone would think I meant you miraculously find yourself in a deep stance. Naturally, a big part of the stance is getting into it and out of it. I just assumed that was rather obvious.I agree with Haruhiko that deep stances in kata were not put in to build strength (a deep stance is low, like a horse can be, but if you're talking about a "forward" stance, there is also a weight distribution factor - I'm not sure how you meant it, but no matter). There are better ways to do that. Stances, like ALL kata techniques/postures, are meant to be functional in a self-defense context. But as this context has been often sublimated in favor of competitive or exercise goals, the intended purpose being lost in the evolution of modern karate to a greater or lesser degree depending on the style.
Then, why is there a low/deep stance? After all, it generally limits your agility. What is its/their value? My initial answer is "NONE." In many/most cases there is no martial value in being in a low stance. The value is found in getting into a low stance. Like any other karate technique, the value is not so much its static position, but in its kinetic motion on its way to that position. This is where the work is done. What work?
1. Early karate had a lot of stand-up grappling. When this is the case a lower center of gravity is helpful. When trying to figure out a bunkai, a low stance is one indicator that some of this is going on. (Here, there is some value in this static position).
2. A lot of times when you grab someone it's with the intention of pulling or throwing him down. Getting into a low stance is part of the technique as your weight doing down adds power.
3. The same applies for a downward strike. Ed Parker called this "marriage of gravity."
4. In the case of a forward stance/zenkutsu-dachi, the process of moving some of your weight to the forward leg can drive it into the opponent's leg, buckling his stance and balance.
There are important nuances with stance work when it comes to kicking as well. There is a myriad of stance/footwork options depending on which leg you are kicking (lead/rear), the direction you are kicking (literally 360°), what you are kicking (leg, body, head), whether you are rotating, etc... The list goes on and on.
But specific to deep stances in floor drills or forms, they do build leg, back and core strength.