> As a non-physicist, QM only clicked for me when I learned the linear algebra of one- and two-qubit systems and observables on those systems

Before quantum computers, the only reason to learn quantum mechanics was so that you could learn to explain the electron orbitals of the hydrogen atom. And after that proceed to understand how other atoms and other matter works.

And for this you need vector calculus, partial differential equations, Schrödinger equation, orthogonal functions (spherical harmonics, Laguerre polynomials) (with hint of the theory of Hilbert spaces).

The idea that someone would like to learn the basic principles of QM without applying it to solve the 3-dimensional probability distribution of electrons around the atomic nucleus, is rather new.