Why is the Foundation of Training so Important?

When I refer to the foundation of training I am talking about teaching a horse the fundamentals of body control. We hear this a lot but, why do we go through all of this work if all we want is for our horse to understand stop, go, left and right? For the most part it is because once we get proficient at these things we usually want to expand our ability and our horses ability.
So why is the foundation so important? Why does it take so long for a trainer to take a horse from first saddle to 4th level dressage? Or why does it take me two years or longer to get a horse ready to show in reining? I guess it is the same reason that it took you 8 years to start learning algebra. You first had to learn the basics.
If you look at it in another context, one that we are more familiar with like yourself, it becomes easier to understand. I often times explain training by comparing it to math. Mostly because everyone has taken math in school, and have an understanding of the multiplication and division. Think back to how long it took for you to learn your numbers and a basic understanding of addition and subtraction. It took longer than 90 days. If it took only 90 days then our summers would have been longer. Instead, it took years for us to understand all of the numbers and have it solid. That is not to say that some of us were able to count to ten before we even started school, but did you really have a firm understanding of what that number represented. Sure you could count and have an understanding of numbers by seven, but could you be held responsible for getting correct change for a twenty dollar bill?
Often times people watch me ride a young horse and see that he can side pass early on and possibly work a little spin. But the real question is does that young horse have a firm understanding of the cues or does the rider have a lot more knowledge in order to help the young horse. It is kind of like the young child when asked how old are you and they look to their parents while saying three. With help and assurance they will get the right answer but if left to figure it out on their own it is a 50/50 chance.
The other reason that it is so important to have a solid understanding of these basics is later on in training, you as a rider can help explain to your horse how to do something better. Lets take stopping for example. While teaching a three year old horse to stop and slide twenty feet. I sometimes have one that will have trouble staying soft on his front end and walk while keeping his rear end in the ground. If he does not have a firm understanding of shoulder control or can not collect and drive into the bit with leg pressure, then I have to go back and teach that. To compare it to math. I am trying to teach you multiplication. You have all of your times tables memorized but are having trouble with memorizing your times tables for the number seven. If you do not understand the value of the number seven, then I as a teacher will have to go back and teach you the value of the number seven. Then I will have to teach you the value of adding the number seven, before I can continue. The benefit is that later on when I am trying to teach you algebra and you start to have problems then I can revert back to your basic understanding of the value of numbers to help you understand algebra.
This is the reason why we put so much importance on the basics. This is why I do not teach or train with short cuts, because it will hurt me and my horse in the long run. It is also the reason why the basics or the foundation of training is the same for every event. Five apples is five apples whether you are in Texas or Japan. In some places you may not want to eat those five apples, but there are five of them none the less.