I try to practice playing some scales every day: C major, G major and A minor pentatonic. Recently I stopped trying to think as much of the position ("string 2 fret 3, string 3 fret 0, string 3 fret 2 ...") while playing and instead think the notes I play ("C, D, E, ...") to associate the position and movement with the name of the note. Then I realised that I have very little connection to the note's "function" in the scale, so maybe it would be beneficial to consciously think "root, second, third, ..." instead?
What would be most beneficial to think while practicing scales?
Similarly, when playing chord progressions from some song: Would I benefit from moving from thinking "C, F, Am, G" to thinking "I, IV, vi, V"?