I should note my description of feedback circuits is a grossly oversimplified, non-mathematical overview of a complex subject. For the curious, read about how op-amps are stabilized, and the concepts of loop gain, excess gain, dominant-pole compensation, and phase margin. Once you get a reasonably firm grasp of how it works, then read about slewing distortion and settling time. I tend to use settling time as a figure-of-merit when looking at op-amps, or more complex discrete circuits.
It all comes together at the summing node, which is simply an analog comparator between input and output. In an op-amp, which has extremely high forward gain, the high gain of the op-amp forces the differences between the two nodes to zero. This is fine until the op-amps clips or slews, which creates very large error voltages at the comparator input. The large error voltage can force the comparator itself into nonlinearity, and feedback theory relies on a distortionless comparator.
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.
This is the gap in existing measurement techniques. Harmonic and IM distortion are averaged over several seconds, and do not sense events happening in microseconds or milliseconds. High-speed scope measurements are insensitive to distortion unless it is very high, such as 10% or more, where it becomes visible. Transient distortions, in the microsecond to millisecond range, are not seen.
The key principle of non-feedback amplifiers is they are insensitive to transient upsets or interactions with the load. Steady-state distortion is higher, but there are no issues with phase margin or settling time.