After reading this entire thread very thouroughly i have decided to recall the original topic starter and perhaps change it a bit. Originally it was asked if ski racing continued to drive ski instruction. The answer to this is yes, but more importantly, we should note what is carried over from ski racing to recreational skiing. I think that most everyone that has replied to this thread has agreed that the main skill common to all 'proper' ski instruction, in some way shape or form involves balance - natural, taught, and learned.
The key to balancing on skis is the realization that skiing is not static (as many of you have pointed out). While it can be understood and described at certain points in a turn by a static diagram/explanation, it is in fact a very dynamic process. An instructor can teach movements to create balance, but it is up to the student to react to what they are taught and use it the best way that they can in order to understand how to balance themselves most efficiently.
Balance on skis is not only complex because it involves moving over an uneven surface, but because it involves balance in a lot of situations and a requirement that you have the ability to react to these situations. This is true for all skiing. Racing aims to teach the most efficient way to remain balanced, as well as recover your balance, so you learn what to do if you are unbalanced. Yes, the ultimate goal of racing is speed, but before a racer ever ventures to learn to go fast they need a strong basis for that speed, and the ability to handle it. While most recreational skiers will never travel at race speeds or require the exceptional balance that a racer requires, there is no reason that this should not be taught to all skiers, or any reason that any skier should not be able to grasp the concept in order to improve their skiing - providing it is taught well.
When hoaning in your balancing skills you will find that there are several places that are 'information centers' that let you know what is going on with your balance and your turns. Remember you have fore/aft, side to side, and up/down all to balance out in a turn. You have the tounge of your boot, the back of your boot, the sole of your boot, your knees, your upper body, and your hands all to worry about. The goal behind ski racing and ski instruction is to create positive movements that put all of these body parts in the correct place automatically - and learning it, so it becomes second nature - so that when something occurrs that causes you to loe balance, you quickly move to recover, and know how to fix the problem - sometimes in a split second.
One key element to balance is the ski. I like to think of it as an extension of my body, so i always know what the ski is doing, so that i can balance myself against it accordingly. Yes, against it. Remember, in a turn you are putting more force into the ski at some angle to the snow than the acceleration of gravity - or you will tip over as soon as you start to angulate. I'm not promoting banking at all, but in a high angulated turn you can pinch all you want and neither of your skis are going to be underneath you... in fact often, neither of your skis are underneath you anyways. You have to learn to trust the ski (particularly, the ski not being underneath you) - as someone else mentioned. This is often the most difficult thing to get used to about skiing, and balance during skiing. You also have to learn to trust the ski on the snow, and be able to manipulate it for various terrain features and snow types - ie. high angulation wont work very well for a bump run, but does just fine on a firm groomed surface. The balance against the ski is a constant motion throughout the turn, and the movements you make and forces that you apply to the ski in terms of balancing are constantly changing. This illustrates that there are no true 'sudden' movements that a skier will make, unless of course it is a recovery movement. I like to think of the ski as a taught rubber band that you push on to make every turn... every turn it springs back and you start a new turn. All of these movements though are gradual movements that apply a constant force to the ski.
One more thing to note regarding racing versus recreational skiing: Carving originated in racing. The shaped ski which came from snowboarding allowed the general public to have race like technique without the effort... merely to make it easier, and ultimately more fun. The idea behind them was to offer a race like carved turn to every skier on the mountain; a turn that was once privilege only to racers.