I believe tubes represent a more even profile of the harmonics, elevating the harmonics in the upper range better than solid state.
This is incorrect. Tube amps tend to make more the lower ordered harmonics, the 2nd and 3rd, which is the source of their 'richness'. These two harmonics are at a high enough level in tube amps that they are able to mask the higher ordered harmonics, which are heard otherwise (if not masked) as harshness and brightness. The class D amp I'm playing at home does exactly the same thing, and since the distortion signature of any amplifier is the way that amplifier sounds its not a surprise that this amp sounds exactly like a very good tube amplifier.