Of course! But the idea here is that probably, at some level, most people are going to need to move across, and not just horizontal. You really need both. You could try and define the whole guitar as diagonal slices, and memorize connections between diagonal slices, but just looking at the lines most people play, I would suggest most people aren’t doing this. I don’t know if it’s technically harder to visualize a connection between two diagonal shapes on top of one another, or sitting right next to another. It’s probably just that people do both, and we need both to really know how to get around in the most common / useful ways.
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Folks like Bruno explicitly do both. Segovia certainly played in position in addition to his scale system. Both of my FordScale scale systems have the hands constantly in motion, but I know my Berklee positions as well and can step off the bus. The diagonal approaches are not necessarily common, but they answer specific problems folks have run into. I would not recommend them for @AGTG in this context as dealing with some of that requires some awareness of music theory. For players interested in jazz on the other hand, I absolutely would recommend looking into them.
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Because you can’t always do that. What if the new chord is Ab, not A? How do you know where the new notes are?
Improvising in the same key, where are the notes are always the same no matter the chord, obscures the core problem a little because you can kind of trick yourself into thinking you’re just using the same fingering and same notes. In actual practice, you may be playing those notes, but your thinking is pretty different. Sure you’re in the same position, but you are now mapping to A. You’re targeting certain notes, maybe using some licks/phrases that only work on A, arpeggios, and so on. Sure same key signature, same spot on the fretboard, but your whole vocabulary has changed.
Move that chord to Ab now and it’s more obvious. You’re not going to simply slide everything down a half step. What if you weren’t even playing in D before, what if you were playing in C major? The half step trick doesn’t even work. Now you’re going to have to locate Ab directly, with your Ab chord shape or shapes, your Ab licks, your Ab scale shape, and so on. All the same things you were playing before. But now, how do you find them?
So again, in the original example, if you truly want vocabulary you can move around no matter the chord sequence, these things need to be wrapped up somewhat independently. When youre in D, and you switch to A, you’re switching to a whole new map - it just happens to use the same notes, and happens to be in the same position on the fretboard. You got lucky! But then that chord becomes minor, or dominant, and now you need to switch up your map all over again.
It’s not really “harmony” we’re talking about, it’s mapping. Whatever harmony you know, you need to know how to find it by some kind of shape mapping system. Personally I don’t even care what system it is, but the core concept is that shapes and intervals which can be moved around is how we navigate the guitar. I feel like we (as a community) have not adequately driven home and explained in plain English why this problem is so fundmental.
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Me personally, I use intervals, and interval visualization.
I was going to say just move your visualization back half a step lol Though you can easily just start a new visualization on the G# note A string, it’s right next to the D.
Am I misunderstanding? I’m no theory expert.
The note names don’t really matter as the intervals stay the same no matter where you start on the guitar. From a C major scale, if it went to Ab aka G#, I’d go right to the nearest G# and revisualize the major scale from that G#. All your licks and tricks remain the same as it’s all relative to the major intervals.
I feel like I’m either missing something in my understanding of theory or being too direct n to the point.
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Yes exactly. Maybe it’s obvious to you but this is a big deal and I went decades without knowing this. I think the fact that you are asking this question and already have your own personal way of thinking about this shows that we are not clearly articulating this as a problem. Same thing with picking technique. Those that had it just thought, what’s the big deal. Everyone else was like, why can’t I do this.
Part of the issue here is that the idea of the interchangeable shapes goes a little deeper than just “find a root note, learn a new scale”. It’s also the connections. That where the money starts to be made. If you need to solo through that C major chord going to Ab, in that same area, you need to rehearse the transition. At first you write a line that is straight up memorized and goes from the one shape to the other. Later on it can be more loosely rehearsed, but either way it is rehearsed, tried and tried again until the transition from the one shape to other is smooth. And then you do it on different strings, with differnet licks, but all in the same position.
To cover the whole neck there, are, at minimum, five or so of these areas to be learned, and in each area you have about five or six different chord types. And then for each of those, you are going to work out connections to and from all the other chord types. It’s a handful but what happens is that the shapes you encounter along the way will start to repeat so there will be some economy of memorization.
Eventually everything links to everything by shape, as you point out, without really needing note names so much as a good ear for intervals and phrases, and a highly detailed map of where they all live.
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That’s the downward slide into the abyss of useful theoretical knowledge that leads to understanding the structural patterns inherent in the scale definitions, away from the physical mappings. 
One answer for when a chord is in the same key, is that you can visualize a pattern that will ultimately overlay the mappings already established for the key, starting on a different root, without shifting. And for the example of A to Ab, if that scale shape happens to reference a chromatic scale, the melodic shape shifts downward as on a piano.
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I’m pretty sure it’s down to not teaching how the guitar works and how it’s tuned. But thank you for the clarification. If I’m getting it intuitively and still so unsure, no doubt there are issues in teaching here.
I hope you guys can come out with some ctc music theory 
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One reason the “play a pattern to go with the chord” approach is limited is that in order for the pattern playing to “make musical sense,” one must still address the question of which notes in the pattern. That means knowing where the chord tones are (or at least intuitively know where they are), and recognizing their function. The related chord shape then becomes mostly superfluous and one is stuck (?) doing what Gambale, Barry Harris, et al., teach. That is, practice running one scale into another over chord changes to hear what works, much as all of the horn instrumentalists have to.
With limited time and resources, we’re all looking for simpler paths. Some of us have been more or less successful with that pursuit on the fingerboard mapping side. But even then, knowing where to put the elbow grease is important and difficult to know without guidance. I wish you all the best in that musical pursuit.
I want to hear chromatic tones in my scales. Even with pentatonics. This tends to turn scales into riffs.
We could list ways to turn scales into riffs:
sequence them
change directions
add chromatic notes
I find it easier to do the reverse. Grab riffs from transcriptions and relate them to the underlying chord scales within and without they live.
I relate riffs not to scales, but to chord areas, or rather, roots of chords which yield “areas” of a chord root. This amounts to about the same thing, I suppose, since a scale contains the chord, and the chord contains the scale.
If I know where the root is, say, D on fifth string fifth fret, then I can see that root in terms of which finger I use to position over it: index, middle or pinky. I think of roots as harmonic, and therefore more related to chord-thinking. Of course, roots are also the first note of a scale.
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