Sorry for the TL/DR post, but you got me thinking (as best I can manage). For those who struggle(d) with CAGED like me… I know the first link is to a Strap website, but I did check others and its largely the same.
From
https://blog.revoguitarstraps.com/major-scale-guitar/
My protege fell into the best/worst thing about the guitar; that is, you can learn a few open chords, a couple power chord shapes, and a pentatonic scale, you’re off and running. The downside of this equation is that you can become a technical master of the instrument while still remaining an absolute beginner in the music category.
I agree with this, and while no “technical master” I could have a lot of fun. I did realise this was not getting me any further, just stuck here. So I tried the following (emphasis mine):
The following five patterns are based on the CAGED system and are the foundation for scale playing. Begin by memorizing these patterns.
I played/learned those patterns, grinding through uncomfortable finger-stretches (I’m old!). I see the same thing on most of the Beginner websites re CAGED and/or C major scale.
I hated it. I hated practice. I didn’t want to pick up a guitar except to go back to a couple of chord shapes and Pentatonic with max Gain that I had any fun. It was only when I decided to shift from Vertical to Horizontal practice that I actually learned all those notes and placements and how to shift from major to minor. I taught myself how to get where I needed to be without finger-stretching pain on those patterns. I move my hand on the neck if it’s a reach.
Learn C major and you get A minor as well. C minor, you get A major, E Major/minor and have G as well.
Standard tuning has E6 as the 5th of A, with D as the fourth right below it. I –IV –V just sitting there. So it’s in A.
The A is the 5th of D, with G as the 4th. So it’s in D.
E minor Pentatonic is the most obvious scale there is on it, so it’s in E minor, which is G major. So it’s in G. Or E.
That’s CAGED pretty much covered - by not following their advice. Sliding non-Barre and Barre chord shapes came “naturally” after shifting from Vertical to Horizontal.
YMMV. I'm no expert, just sharing my personal struggle with CAGED, which I have overcome. It's a popular system, so it may suit you perfectly.