Distortion of monophonic tones (single notes/voices) became accepted in the mainstream quite rapidly because the circuits used to produce it quickly improved, informed by feedback (no pun intended) from musicians.
Nobody hates ugly sounding distortion more than he or she who practices 5 hours a day with it.
Single note distortion, at its best, is a harmonically rich sound which shares something with bowed instruments and reed woodwinds.
Nasty sounding single distortion has not gained complete mainstream acceptance. Musicians who do that on purpose will remain niche, even today. From time to time, such nasty sounds make appearances in mainstream pop, but only as a kind of "cameo". The statement is, "we are inserting this ugly thing here specifically for its idiosyncratic effect, haha! But only a few seconds, we promise".
Distortion (other than perhaps mild distortion) has never been fully accepted in roles where the multiple voices of a complex harmony part would be distorted together.
Nowhere was that better seen than in jazz/rock fusion, which accepted ragingly distorted guitars for solo work, but not so much for the rest of the music: except, of course, in passages where the guitars provide the "sound of rock": distorted fourths and fifths and whatnot, or double stop bluesy cliches and whatnot.
The music best known for distortion and that couldn't exist without distortion (and a lot of it) is of course heavy metal, which is a big landscape of styles and sounds.
In metal, the harmonies from an individual guitar part tend to consist of only a few notes. The clean chord is transformed into something else, which perhaps cannot be described in music notation. Complexity comes from the distortion. Distortion includes the sum and difference products, which relate to the tonality and scale of the music in unsual ways. Those notes are not identified. If notation is used at all, the underlying clean notes are notated: e.g. C-F# tritone on the A and D strings, over open E bass. Heavy metal uses syncopated and alternating rhythms to separate bass notes from upper notes in three and four note chords. This is not only to create rhythmical excitement, but to better separate the notes.
The notes of a distorted chord are also easier to for the ear to identify if they are introduced separately as a lasciare suonare arpeggio; that's a thing in metal.
Harmonic textures are also created by combining distorted guitar parts. Using two lead guitars originated in rock, with groups like Wishbone Ash. Multitrack recording allows an unlimited number of parts to be layered.
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