When I analyzed the CAGED system, I think it can be
simplified into just three (3) shapes. The D and C can
be combined. The A and G can be combined. And then the
E shape. So we have 3-shapes namely the D/C, A/G and
E.
Inside these three shapes are found the patterns of
the major scales. Cool huh??? What do you think?
As a guitar teacher dedicated to illuminating the details of music theory for guitar, my goal is to break things down to the basic building blocks and then show guitar players how to develop from there. It sounds like you're on the right track.
The five CAGED chords can actually be simplified into just one shape. In fact, it IS one shape that covers the whole guitar fretboard. It's broken up into five pieces, or forms, so that you can learn and memorize it one step at a time. Eventually, if you learn lots of CAGED songs and apply the chord forms and arpeggio patterns to music, everything begins to bleed together. At that point, you can group the shapes however you see fit.
And yes, major scale patterns can be played inside any and all chord shapes.
The practical application of guitar theory will be thought of slightly different from player to player.
Play Until Yer Fingers Bleed!
Mr. Desi Serna (Google me!)
http://www.Guitar-Music-Theory.com
Pentatonic/CAGED/Progressions/Modes