From that point of view, the interesting thing would then be why this particular abstraction layer works well which is what linear algebra answers.

This is in some sense the process all math students go through. The formulas for computing determinant and multiplying matrices look really complicated and it feels like a mystery as to why it works at all but then linear algebra explains all of that slowly.

Perhaps it would help students to start with an application before digging into the theory. Coordinate transformations might not be too forbidding for high school algebra students, especially if aided by some math software or a Python notebook.

As a programmer, I see real numbers as a leaky abstraction. In general, they cannot be represented, but they make the formulas prettier.

Not trying to be snarky, just an observation.