More often than not, I've found tube amps that use feedback sound more realistic and are more compatible with wider range of speakers than amps that use no feedback. I've looked into why audiophiles think no feedback is sonically superior, but I can't find any good reason to support this contention. Yes, NFB does increase odd order harmonics but the levels are low, and I doubt if anyone can actually hear them reliably. I've found most tube amps with no feedback to have less controlled bass, less dynamics, and subtle softening of the highs.
I did not state an opinion, but fact. Nor is it something I made up- this has been with us for a long time. You might want to read the article that I linked.
It is quite true that there are more speakers designed for amps with feedback than those without. And its also true that if you use an amp with no feedback (Power Paradigm) on a speaker that needs it (Voltage Paradigm) you will get a tonal coloration of the types you describe.
You are incorrect in stating
the NFB does increase odd order harmonics but the levels are low, and I doubt if anyone can actually hear them reliably
The fact of the matter is that slight increase in odd-orders are described as 'bright' harsh' 'hard' 'clinical' etc. by audiophiles, yet we are talking about distortion levels that may only be increased by a few 100ths of a percent! This is because the ear/brain system uses odd ordered harmonics to sort out how loud a sound is.
This is why two amps can measure flat on the bench, but one might sound bright and the other might not.
IOW the ear is considerably more sensitive to these harmonics than it is to human vocal frequencies.
General Electric proved this back in the 1960s- its not anything new.
Again I recommend you read the article and most of this will be made clear.