if we reduce the question to the most basic/simple form, the answer is a giant and resounding
YES, WE DO CRAVE DISTORTION.
Very simple proof: just listen to a
pure sinewave compared to a
piano note (of the same frequency). "Surprise": ~everyone prefers the piano note and hates the sinewave.
One of the major extras that make the piano note sound much more pleasant is Distortion: i.e. it contains 10+ HDs which contribute to its pleasant piano-timbre (and make it sound different from the same note played on guitar, trumpet etc...). A nice video
explanation.
Another simple proof: every instrument/note contains 10+ HDs, i.e. >90% music is actually distortion/HDs. And then you add a giant amount of IMD products and reach >99%.
I.e.: >99% percent of what we call music is actually made of 'distortion'.
So yes, we do crave distortion. We listen to it everyday. And if it's taken out, we just hate it. (if you don't believe that, good luck listening to music made out of pure sinewaves)
Extra distortion added during playback is a different question and quite a bit more complex. But the fundamental rule is the same: the human brain likes and demands the 'distorted' sounds!
It's 'just' that we do not know very well which kind of extra-HD is liked/hated .. and that lack of knowledge is the source of a million audio-forum posts about distortion (many of them less than useless).