What does correlate with sound quality is the harmonic structure of the distortion that is generated...the order of the harmonics and their relative and absolute levels. This has been known at some level since the 1930s but was largely ignored once negative feedback pushed all naysayers away into a THD arms race.
Nelson Pass thinks different - his anecdotal studies have a third of folks preferring 3rd harmonic. These are probably the same folks like Frantz that find an unnatural "beauty" on many SET amps. I have to admit my last two SET demos had me thinking similarly.
http://www.firstwatt.com/pdf/art_dist_fdbk.pdf
I'm not saying there is a right or wrong way - but I don't think its as simple as you think. I also don't think there is a THD arms race in 2016. Many high end amps use little to no negative feedback as well.
I also *strongly* believe in amp/speaker synergy and an amp that may sound great on one speaker, doesn't work on another. Luxman Class A, for instance, sounded like cream on my Zus - but works very well for Vivid speakers.