My musical development has been tremendously influenced by chord scale theory (CST) though I never went to a music college whatsoever. I self-studied through books, articles, youtube, forums, private lessons/classes, and gigging. Levine’s The Jazz Theory Book was the gateway book for me back in 2000 when I was 19 years old and semi-interested in classic jazz.
I fell for the Levine-CST bag hook line and sinker. I spent years tracking down almost every recording in the footnotes, had a pianist friend play all of the “two hand” examples. And even went through Levine’s piano book to get piano-like voicings on the guitar.
Though, I liked Levine’s work, something always bothered me… a few things in fact. His neglect of the harmonic minor scale and exclusion of functional harmony (no mention of secondary dominants, melodic devices, guide tones, etc). At this point, I began to use CST in my own way based on my ear and what I was hearing in actual music (jazz and non-jazz alike). I naturally had a sense of the tonal hierarchies within a chord-scale. I heard the tonic, basic triad, guide tones, tendency tones, extensions, triadic upper-partials and so on. It never ended with the idiot-proof “play this over that, avoid that note” BS. That makes no musical sense and no one in classic jazz thought that way. I have turned away from Levine and found Bert Ligon’s books much better all around.
I don’t think throwing the baby out with the bath water is a good answer… Let’s turn to rock improvisation. I work in a guitar store (over 10 years experience, now a manager), and I have been teaching guitar lessons that long as well. It is typical for students (and some professionals) to ask “what scale do I play over that SONG”. They want one pentatonic, blues, or full diatonic scale that fits the entire progression, and then they want to noodle and shred from there. The idea of chord-scale pairing is beyond their wildest dreams, and a tonal hierarchy within each is out of the question. CST is a way to get lead guitarists (or other melodic instruments) to pay more attention to the underlying progression. A progression that “borrows” parallel chords via "modal interchange" (common in Beatles tunes, jazz, hip-hop, grunge etc), back-cycling (country western, rhythm changes, sweet Georgia brown, etc), secondary dominants (most "functional" progressions), makes the “one scale” idea is nearly impossible to pull off. Note that “harmonic generalization” is very different and melodically complex compared to "noodling" in one key.
There are huge pitfalls to CST as it is usually presented (CST without tonal hierarchies), yes, but I still feel like it is a great launching point (though tedious to grasp at first for those without exceptional patience and memorization capabilities). There are no true short-cuts, but going the long route without CST seems even harder and creatively limiting. I cannot imagine playing a Wayne Shorter tune or soloing over the changes to “Strawberry Fields” without it.
At this point I can solo over any oddball chord progression in a harmonically specific way that implies everything between the counterpoint of my part against the bass line (no chords needed). That’s where “linear harmony” comes in and fills the gaps of CST, and allows the rules to be broken (not “outside” mind you) in order to give the music direction; the elements of rhythm; especially “harmonic rhythm”. Chromatic notes, anticipations, and melodic devices make a lot of sense on this level. Again, this is miles away from the typical rock/pop guitarist’s one scale mentality. Thoroughgoing CST is very different than memorizing the dictionary!