Sorry that was vague. I was just talking about ma7, min7, dom 7, 1/2 dim, and diminished chords. Practicing them diatonically as you said is a great way to hear the chords in the scale.
but I think if the concept were taught as "understanding tonal centers" rather than "learning scales" it would be a lot more useful.
Absolutely. I try not to think of scales from root to root, but rather from the lowest note to highest in that particular tonal center. You just need to know where the half steps are. Mick Goodrick says it best when he points out that the half steps of any mode have the potential for the most color and/or dissonance.
Hopefully I am not taking Carol Kaye's quote out of context, but I think scales get a bad rap. Look at Donna Lee for example. Starts with a descending Ab major scale melding into an implied Bb harmonic minor scale getting to the 3rd of the f7. It goes on to outline the b9 and #9 of the F7 descending to the 3rd of the Bb7 arpeggiating up to the 9th. The key here is not scales and chords, but being aware of targeting notes within both contexts.
I like talking about theory, but really, it is about internalizing all this stuff so that you can improvise creatively. Someone said that if you take a Charlie Parker tune a month and learn it in every key, you wouldn't have to know anything. You would have all the melodic, harmonic, and (most importantly) rhythmic vocabulary down.
All of the above is in context of playing an improvised solo, not an accompanying bass line.