I just had a revelation about the triads.
There are three per string through fret 12 and four across the fretboard from the sixth string through the first, for a total of twelve positions for each triad on the fretboard (up to fret 12).
For anyone who has studied CAGED or any other system that allows you to improvise all over the fretboard, this is many orders of magnitude more liberating. At any given moment, you know 12 places on the fretboard you can move to in order to "nail the changes" if you're playing jazz, and also 12 different places to solo over the same chord if you're playing blues or rock.
If you practice all triads in all keys, major and minor, every day, your familiarity with the keyboard will be ... well, it'll be like Tomo's. Look at how he can instantly spell any triad in any position, not only naming the notes but also the degrees of the relevant scale, even switching between scales and naming the notes according to the different degrees, e.g., calling CEG the root, major third, and fifth of CM, but also the minor third, major fifth, and dominant seventh of Am7, or even the ninth, eleventh, and thirteenth of Bbm. (He does that in one of the triad videos.) He does it without batting an eyelash. It's instantaneous. It's amazing.
My mind is officially blown.