FWIW, I was told that matrices are linear maps pretty early on in my education. Are there any college level linear algebra / matrix calculations courses that don't tell students about that?
When I went through university the standard set of courses was a Calculus course that was mostly about derivatives, a second one that was mostly about integrals, a third Calculus course that was about multi-variable Calculus. That third course necessarily had to teach matrices, and taught it as rote calculations. There was a follow-up differential equations course which refreshed people's memories of matrices..as a rote calculation.
It was done this way because the multi-variable Calculus course was a prerequisite for a lot of physics+engineering courses. So a lot of students wanted to take that sequence. Differential equations were a prerequisite for some other advanced courses. Linear algebra was pretty much just for math majors.
I took Linear Algebra the same semester I took Computer Graphics, which worked out really well for me - the first half of LA taught me everything I needed to know about transformation matrices, and the second half of CG covered 3D graphics in OpenGL. The first half of CG was all 2D graphics stuff, and the second half of LA was about eigenvectors/values - I've forgotten everything from that part of the class.
I know they taught us about matrices in high school, but I don't recall them talking about any applications at all. I think the topic was pretty drained of context, just rote application of the rules for add/subtract/multiply/etc.