Scott Aaronson does follow a similar line of thinking in this Quantum Computing Since Democritus lectures [1]. He talks about the p-norm aspect, but doesn't talk about the tensor product structure. And I think for good reason. The way I teach is good for learning, but it is not how you would ultimately think about the link between classical and quantum computing, once you become an expert. Then you should think in terms of complexity theory or in terms of axiomatic relations between classical and quantum theories or information theory principles etc.
There is also David Mermin's book, which has a section on a similar sort of reasoning. I don't recommend it as a self-learning book because it has no exercises.
This is very much becoming the "standard" way to teach quantum information science.