When I was in grade 11, I was fortunate enough to attend a high school that offered an optional course in vector geometry. The course was taught out of the book Analytic Geometry with an Introduction to Vectors and Matrices by Murdoch. The high school course covered the first $2/3$ of the book, so it didn't really deal with matrices.
After that, my next contact with linear algebra was in a highly abstract form as an undergraduate in Europe. (To give an example, the proofs of the theorems on kernels and images of linear mappings appealed to the analogous facts about groups. Matrices were introduced after linear mappings, quotient and dual spaces, etc.) This was made possible in part by the fact that my European classmates had all studied vector geometry the way I had as part of their normal school curriculum, and perhaps even more in depth.
In any case, I never really experienced the typical beginning linear algebra course most Americans do, so when I eventually had to teach one a number of years back, it was something foreign to me. I taught a college linear algebra course out of Elementary Linear Algebra by Anton, the compulsory textbook. I was shocked that my students' first contact with linear algebra could possibly be so ungeometric. The chapters on matrices and determinants came before the chapter on vectors. Had I not made significant changes to the presentation of the material, much of the work on linear equations, matrices and determinants would have been unsupported by what I thought were indispensable geometric interpretations.
My questions are as follows.
Do college teachers agree with my feeling (a hunch, really) that the typical approach to linear algebra in the U.S. that deemphasizes vectors until a late stage is likely to compromise non-specialist students' ability to use linear algebra in later studies and in real-world applications?
If so, what is the impediment in the U.S. to shifting vector geometry to an earlier stage of the high school or college curriculum? Could there ever be an AP Vectors?
Could it be that the study of mechanics acts as a kind of back door to facility with vectors for science students, but students going on to economics or social science are handicapped because they never get an equivalent opportunity?