As a psychiatrist, I hear about "depression", a lot. Its use is so pervasive that one would assume we're all talking about the same thing. However, to someone who specializes in treating depression, it means essentially nothing. Nothing, without more information.
Depression could mean many things: a synonym for sadness (a normal human emotion), short-hand for a psychiatric disorder (major depressive disorder or bipolar depression), grief or adjustment to stress, a reaction to a medication, or something completely different from what the word actually defines: hopelessness, loneliness, emptiness, despair.
To treat "depression" without empathy or understanding of the person's narrative could be a foolish exercise. Your idea of treatment maybe helpful, you could get lucky. For example, if you assume someone's depression is truly a manifestation of major depressive disorder. But, what if you're wrong? What are you treating then?
A fear of mine is that the meaning of depression is evolving from a word referring to severe melancholic sadness to a state of hopelessness, frustration, or emptiness. These latter conditions require a much different approach, all of which, necessesitate empathy for the unique experience of the condision. A scale will not do.