The only question here that is open to debate is whether the crossover distortion of a well-designed Class AB is audible. If the answer is decidedly "no", then this immediately becomes a silly debate. Anyone who wants to claim the superiority of Class A needs to offer evidence of the audibility of distortion in Class AB amps, not cherry-picking some poor example, but ideally showing that even in the Class AB amps that measure among the best of the breed, crossover distortion remains audible. And we should all know by now that to do that, it is necessary to prove it using properly controlled blind testing protocols. Of course there will always be a few people who will immediately perk up and offer the exceedingly tiresome argument that blind testing is worthless if doesn't agree with what they "know" that they hear. When considering the question of audibility of distortion of Class AB, I would maybe pay some extra attention to distortion at low volume. I don't know ... it's the only thing I can think of where there might be a possibility that Class A has an advantage. I'm sure that there are people here who have a very good understanding of this question and should be able to shed some light on how THD + S/N breaks down into THD and S/N at low playback level, and whether there is an inherent difference between Class A and Class AB with respect to accuracy at low playback level.
It also occurs to me that there are other similar questions where an open discussion might be more informative. One example I can think of is the question of whether "soft clipping" is commonly implemented in amplifiers, and if so, whether it is particularly likely that actual distortion levels may be appreciably higher than people generally take for granted, owing to either (a) masking of distortion by the soft clipping, or (b) the soft cliHI pping itself.