The harmonic profile has more to do with the amplifier architecture than open loop gain. Differential and symmetrical push-pull stages will naturally cancel the even order products.
True, but NFB lowers all distortion components, including even order harmonics, should they exist, regardless of architecture. However, even though it acts to lower *total*HD (the sum of all harmonics) the individual odd orders are increased in level. As the human ear/brain is more sensitive to ever lower percentages of harmonics as the multiple increases (eg "high order harmonics") this can result in an audibly less pleasant sonic quality.
For example, given an amplifier that measures at 1% 2HD, 0.5% 3HD, and unmeasurable 4~9HD, the THD would be roughly 1.5%. As H2 and H3 are natural components of musical instruments, they are perceived as un-objectionable by the listener. The effect might be to blur the sound ("tone") of a Hammond Concert Grand piano so that it might sound similar to a Yamaha Concert Grand, but will not be unpleasant.
Apply NFB, and the measured distortion might be 0.1% 2HD, 0.05% 3HD and negligible even order HD from H4~8 (total 0.15%) but may also have odd order H3~9 of 0.1% where none existed before, resulting in perhaps 0.5% THD. The effect may be to make the sound clearly a Hammond but a Hammond that doesn't sound "right", as odd order harmonics are not always related to the fundamental in nature.
A seemingly large reduction in THD but with a more objectionable harmonic profile.
Another look at the issue we can explore music created prior to the mid-1990s to a certain extent and prior to Ry Cooder's "Bop Till You Drop" album of about 1978~9 in every extent (that album was the first released with digital recording, mixing and mastering, versus recorded on magnetic tape)*. The nature of magnetic tape is, although pro level decks were capable of low distortion with SNRs of 65+ dB (90dB with DBX encoding), if you look at the harmonic profile, the H3 would be prominent, as that is the primary distortion characteristic of magnetic tape.
Now, I don't know too many people who think their Led Zepplin albums sound "bad", even though there is a relatively strong 3HD component to the entire recording. (Originally, when mag tape was first introduced an became popular in the 1950's, the "THD" spec referred not to total harmonic distortion, but to third harmonic distortion).
Clearly the distortion profile, together with the total distortion level, is important for our enjoyment of a recorded performance.
* I often wonder if there wasn't a transfer to 2-track, as there may not have been any record pressing plant that could accept any other format at that time.
