That is not distortion - or is a silly definition of distortion:
Distortion is a change to the waveform. Think of *any* acoustic instrument, or the human voice.
The waveform comes from those instruments fully formed with the fundamental, and all relevant harmonics to create the tone and timbre of that instrument.
That is just an oppinion/point-of-view. It's somewhat fair, but I do not share it much.
The math does not share it either: a harmonic signal added by an instrument or by any other means is exactly the same thing. There is zero math-difference between 'artificial' amp-HDs and 'natural' instrument-HDs, so it's mathematically improper to call/treat them differently.
Musical science/theory does not share it either: a harmonic is defined as a multiple of the original frequency. That's all, it doesn't matter who/where/how generated it.
The human ears do not share it either: whatever way a harmonic signal was added, it has the exact same effects on your ears/brain/perception.
Simple proof: a modern/good synth generates all the piano HDs 'artificially' and sounds exactly the same as the acoustic piano (which generates the exact same harmonics 'naturally').
The fundamental has never existed standalone in order to be distorted.
The instrument *cannot* create a sine wave, and it certainly doesn't create a sine wave and then distort it.
That may be true for acoustical instruments (btw, do you have a citation/paper?)
But an electronic synth does exactly that: it does "create a sine wave and then distort it". And it sounds the same as the 'real' piano.
Even if true (for acustical instruments), your argument makes zero difference for the human ears/brains (also none for the physical air-waves).
Distortion then is anything done to that original waveform that changes it. In terms of reproduction gear (which we mainly discuss here) that comes from uncontrolled non linearities in the process. It results in a reduction in the accuracy of the reprocution of an instrument's (or voice's) timbre.
You call the HD "reduction in the accuracy" and you have a fair (engineer's) point of view.
Some people may call it "more musical" and they have a fair (listener/musician's) point of view.
Maybe you should stop calling other people's point-of-views "silly".
Especially when theirs seem to be well supported by math, musical science and human physiology. And yours is supported by ... well, not sure what besides the EE-book definition of 'distortion'.