Hi! First of all I'm still a beginner when it comes to the scales (more so, in music theory and improvising) so this might not answer your questions directly but I'll try to share a little of my experience.
Before joining this forum I was trying to learn the minor pentatonic scale and its different positions along the fretboard because I wanted to add something ("improvisation") to my guitar playing which has always been on strumming, then humming the solo or the riff portion, while playing the chords. So after I joined here, I was exposed to another "school of thought", which is, improvising by the use of chord tones. Although the choice between using the scales and using the chord tones is up to the person who plays the guitar, I felt I was convinced that the use of chord tones will work better for me than using the pentatonic scales.
So what to do with what I learned on pentatonic scale? I still find it useful as a warm-up exercise, for finger stretching. On the three notes per string you mentioned, usually the third note on the string can be "relocated" to the same note on the next higher string (or looking at it in another way, the first note on the string can be "relocated" to the same note on the previous lower string), depending on the convenience of your fingers. Also, I believe that the letter names of each note of the scale will be helpful if you are into memorizing the notes on the fretboard.
So there, I know there are a lot of scale players here who can explain it better that me. Good luck!
