Most of us would agree that the SAT is a "different animal." But what do we mean? It's not like schoolwork, not like a test you may have to take in your Algebra, Geometry, or Calculus class. So, in a way, very few students are actually prepared, since much of the material may be presented in an unexpected way.
Years ago when I was teaching High School, I would often include on a test, one problem (maybe for extra credit, maybe not) that my students had not seen before. It would require applying what they learned, going a level of abstraction above the specific processes that were taught. Many of the SAT Math questions fall into this category, and both students and parents ask--why? Why are they torturing our kids, who work so hard for their GPAs, and then have to take on additional challenge? Why isn't SAT Math taught in school?
There are several answers to this question: First, the "A" in the SAT stands for "aptitude," which is different from "achievement." Many students can achieve high grades by working hard and memorizing methods of doing problems, or even by doing lots of extra credit work. Arithmetic, basic Geometry, and beginning Algebra can be learned in large part by how-to. But, advanced word problems and complex Algebra cannot. While some basic problems are included in the SAT, the makers of the SAT are testing for skills that go beyond how-to, testing a student's deeper understanding of concepts and how the pieces fit together.
Second, schools are already extremely pressed for time in covering required topics, and typically might not have time to work on test prep during regular school hours. A third consideration is that practice is an important component of preparation, and practice also means time--possibly lots of time--depending upon the student's goal scores.