What you are saying is correct from an engineering standpoint but it completely ignores the human psychology.
Tube amps produce a lot of (not only harmonic) distortion, especially the cheap stuff. And then there are also various nonlinearities due to the inevitable transformers, tubes aging, mains hum, etc.
The problem is that musicians (and not only) were "raised" on this type of "sound". So they consider this to be the nominal, "correct" way how an amplifier is supposed to sound like - especially that one obscure box they got 40 years ago at a garage sale somewhere is the gold standard.
They don't know squat about harmonics, distortion etc, many barely understand that the blinking red light on the amp indicating clipping is not what one is supposed to see and not the signal level one is supposed to adjust the gain pot to.
But they then see that a clean solid state amplifier (or even a tube one with a lot of negative feedback and compensation) sounds different, thus it has to be the one that is "wrong" and "sounds bad".
That's where the myth about tubes sounding "better" comes from. It has little to do with actual measurable distortion value.