It doesn't mean you cannot build a nice amp that uses NFB, but that "air" and sense of "realism" that you treasure is hindered by NFB.
That depends on how the feedback is implemented!! If the feedback is sent to a non-linear point in the input of the amplifier which is used as a feedback node (such as the cathode of an input tube) then you can expect it to be problematic, as Crowhurst pointed out 60 years ago, and Baxandall 'rediscovered' 15 years later.
In other areas of electronic design, feedback is known as 'control theory' and is very well understood. But in audio, it seems to get misapplied (and so gets a bad name) on a regular basis, then everyone points at feedback being the problem when its really just design flaws.
In addition, if the comparator is saturated, or if the power supply sags or is discharged, then recovery time can be quite long (tens or hundreds of milliseconds), much longer than the original clipping or slewing event.
During this settling time, amplifier distortion can be quite high, since feedback is only partially effective. This will not appear in FFT harmonic distortion or multitone IM distortion measurements, which are taken over several seconds and then averaged.
The settling time referred to above is a process of many amplifiers with feedback, but not so much opamps (unless overloading, which is easily avoided). In a nutshell, the reason you run into the problem described above is that part of the amplifier circuit is not in the feedback loop. So it can behave as described and as pointed out, lots of test equipment ignores this phenomena, although it can be measured if you have advanced gear. There is more at this link:
https://linearaudio.net/sites/linearaudio.net/files/volume1bp.pdf
If you don't want to read the whole thing, start at page 11, where the math is a bit lighter- but stay with it till the end of the article- its all relevant to this conversation.