Here's the thing though.
A musical instrument has an attack, sustain and decay in which the harmonic content even changes. At each certain moment a 'tone' has a harmonic profile that chances in the next moment.
An amplifier adding harmonics does not have attack, sustain and decay but has an harmonic profile. That profile is somewhat level dependent as well.
The thing that also separates an amp from a musical instrument is that not only each fundamental but also each harmonic (of the original sound) gets their own harmonics added.
If that were the only thing that was added one could live with that. Unfortunately an amp also adds IM products from all other tones and those aren't harmonic at all and can create signals that aren't masked by the musical notes. They form a kind of modulated noise floor (clearly seen in multitone measurements). This is not what an instrument does. Sure it can beat and produce IM but not in the same way an amp does.
So ... an amp is not a musical instrument. It can not 'generate' sound by itself the way any instrument does (unless it oscillates

) it can only amplify and change the applied waveform a tiny bit.
O.K. ... a tube amp can be played like an instrument by tapping the tubes but have not any seen musicians do that, probably because it will be hard to tune the vibrating grid(s).
In the end the best reproduction is when nothing is added.
That harmonic profile of a certain tube or even a tube circuit can be emulated in software... when that is done can that be indistinguishable from the circuit it is imitating ?
If so there is no 'magic' in tubes but it is just an altered signal.
What other signal is there other than the signal in the electrical plane ?