It's very important to note the difference between THD and relative amount of harmonics.
THD is a technical measurement which gives rough idea how linear a component is but it doesn't tell much how it sounds like.
Harmonics and their relative amounts needs to be inspected to relate measurement and "real life"
Like you said a flute would sound like oboe if level of 5th harmonic (lets just say 3%) in amplifier (amp 1) would match that of natural sound of oboe. However another amplifier (amp 2) with equal amount (3%) of second harmonic would not make flute to sound like oboe at all. How would it sound then? I can't answer that but generally 2nd harmonic is considered as pleasant and thus might not be so critical at all and amp 2 would be greatly preferred over amp 1 as source of natural sound even though they both are "technically" equally "good".
What's really interesting is which amounts of distortion and what kind of relative distribution between harmonics is acceptable or even maybe preferable.
Many tube amps "excell" in higher even harmonics and relatively minor amount of odd harmonics. Maybe bit of "natural" distortion adds to close miked dry studio recordings