I like what you said there.That aside; I would think that the ONLY humans who can unequivocally answer that question (re: good distortion) are those in the production-side of the music. Anything else becomes a subjective criteria of added personal "preference".
I know a great deal about the production side of music, (without that being my profession), for a number of reasons, but I can tell you on the production side that very little, if anything, is chosen based on science, objectively or measurements (except possibly monitors). With the best of the best it was trial and error, watching and learning and their own individual preferences. Time and time you will hear the top in production say things like “I like a Neumann this, for that I always use the Shure that.” “Why do you like [fill in the blank with microphone, compressor, limiter, reverb, technique]” and the answer nearly always “well I heard a [fill in the blank] when I recorded/mixed [previous project] and I like the way it sounded.” Sometime followed by “audiophile” type adjectives.
For distortion, the good ones will know specially how each type of distortion alter the waveform, at what harmonics, and they have been blessed with ears that what they think sounds good is generally thought to sound good by the artist and the public.
It certainly is salt/pepper preference, assuming it isn’t analogous to what is measured on amps.