There are benefits to practicing the shapes of the guitar in a horizontal way. Moving up and down the neck with ease allows you to shift into new positions more accurately, and practicing many different patterns horizontally allows you to find the notes you want in each position.
Practicing a new scale or arpeggio by isolating the pattern on a single string can help the ear become more accustomed to the new sound, removing the element of position-based thinking that typically accompanies new pattern learning.
When the same scale is played simultaneously on multiple strings, it becomes the chord scale. You can make many different types of chords out of scales, from duads (doodads?) to cluster voicings, chords built in 3rds, 4ths, 5ths or any other conceivable way, but every one of the types of chords can be moved through the scale it is derived from to get IT’s chord scale.
This video uses chords from the key of G major played on the 2nd, 3rd and 4th strings. Beginning at the root position voicings, the 4 exercises that make up this workout present different ways to practice the chord scale in G major, utilizing many of the notes surrounding the chords in the scale.
Video has a full explanation of all the chords and a detailed description of each exercise. The full workout is here at 3 different tempos for those who want to learn the exercise and work it up. I promise it won’t make you any worse. If you practice it with an emphasis on playing with a strong time feel (feeling the first note of each grouping) you could most probably become better by doing this.