Arnheim is kind enough to distinguish between "generative complements" and what he calls "fundamental complements", (though I would prefer they be called "perceptual"). He warns specifically against confusing perceptual color and color-in-the-world. By making that distinction, Arnheim validates BOTH systems, rather than attempting to invalidate three-primary systems (as this article appears to do).
The article calls RGB and RBY color "wrong" and unable to "stand up to even minor scrutiny".
Arnheim calls them "generative".
I claim their generative nature (that they inform how to create color) is why they are taught in schools. I'm not denying the four-color idea; I'm just saying it is based on a different definition of color, and different intended use of color.
I suspect that we continue to teach the RGB, RBY, and CYMK color wheels because they behave correctly with respect to the behavior of particular physical media. Yellow-looking paint and blue-looking paint do make green-looking paint. Red-looking light and green-looking light do make yellow-looking light.
The (physiologically accurate?) four-primary-color model proposed here does not correctly predict the world: yellow and blue act as additive color opposites; red and green act as subtractive color opposites. No one set of pigments or lights will ever consistently behave the way this 4 color wheel predicts.
We need multiple systems because colored objects mix by multiple mechanisms.