"Perspective distortion is the natural result of trying to impose a 3-dimensional world onto a 2-dimensional image"
Yes, but the intensity with which it is going to occur within the photo is depending on the focal length and the distance between the camera and the object, too. Try to make a photo of a tall tower, using the 500mm telephoto, for example, and do it from a distance which is just enough for the frame to be filled. Let's say it's a 1 mile. You'll get alomost perfect perspective. Now try to fill up the frame with the photo of the same object, using the 28mm lens. You will have to come closer, and you will inevitably end up with the distorted perspective, right?
And I got to add that longitudinal CA and lateral CA also belong with the optical distortions (specific behavior of different light wavelengths traveling through the lens), not just barreling, pinchcushioning and "mustaching" (like you wrote)...