From my reading, I am aware of another consideration in these matters. The way an amplifier circuit reacts to very high frequencies presented to it, frequencies too high to be heard on their own, can affect the behavior and sound of the amp. A barely-stable circuit can be driven into oscillation by those frequencies, creating ringing and different forms of distortion.
Frank Van Alstine and Roger Modjeski have discussed this area of amplifier design in their writings, and it is an important consideration with ESL loudspeakers. They benefit greatly from an "unconditionally" stable amplifier. Both Frank and Roger make such amplifiers, though they are not alone in doing so.