Open any old Karate book, Karate-do Kyohan the Bubishi. Books where the images are black and white or even a few modern books and you'll find small stances.
Ginchin Funakoshi, founder of Shotokan.
We look at these stances with today's eyes and think how weak they look but here's the thing. Those are the true stances and you'll still see schools training in those shorter stances today. We reference them all the time. So why then do we and so many major schools train in these long deep stances.
It's for one simple reason, Longer=Stronger.
The longer of a stance you train in the stronger and more flexible your legs will become. Within reason of course.
One needs to gradually lengthen their stances over time as they continue to train and maintain mobility in them. The concept is, if you can move fluidly in a longer deeper stance then moving freely in the stances true form becomes easy.
The idea is similar to that of any other practice of a technique. Training to it's fullest motion for its maximum potential.
Think of it like ringing out a damp rag in one twist. The rag is the technique and the water is its potential power. With each throw of a technique you're trying to ring out as much power as you can. We of course practice control throughout our training because more often than not we'll need to hold back our power output. The question is, in a combat or self defense situation should you have the opportunity to use a technique to it's fullest will it be there? Well, if you train properly it will be. Same goes for your stances. Train strong and you'll perform strong, train weak and well you get it now.