> The word was originally used to describe the decomposition of waveforms into sums of sinusoids, which is as canonical an example of a linear system as you can get.

You are right, I was being a bit too sloppy with my usage of the term "superposition". I guess once people realized that a QM system being in "two states at the same time" is just a linear sum like for waves, they started calling it a superposition. Anyway, my point (in my original comment) was a completely different one: You still have to assume all that linear structure to start talking about how canonical the tensor product is.

> But that's not what's going on. A system is only ever in one state at a time: the ability to treat it as a sum (modulo the norm) of other states is linearity of all operators

Again, you are right, that's why I put it in quotes. Nevertheless, if we start just from the observation that a system can occupy two states "simultaneously" (in the sense that sometimes we measure one, sometimes the other state) we might think of other ways to encode that beyond vector sums, e.g. Cartesian products without any linear structure.

Anyway, I don't think we disagree fundamentally, we're merely arguing about terminology.