Not so! The gold standard treatment includes CBT, which acts on thought patterns.
Trying to separate thoughts from the physical brain wiring is futile - there is no disconnected "thought" that is _not_ the wiring of the brain. Changing thoughts does change brain, and changing brain does change thoughts.
I'm not sure how that helps. If we identify the precise biological markers that correspond to depressed feelings, does that help us in some way to change them? We already know these people have depressive emotions, it's not like this test would reveal something we didn't know about them. There is clear value in this from the scientific side, but I don't see how it would help with treatment more directly.
Conversely, if we find biological signs that are not directly related to currently experiencing depressive thoughts, those could be a promising target for medication/therapy, and could help detect depression earlier or in more borderline cases.
Consider patients that present with general malaise, fatigue, lack of motivation, grumpiness, etc.
Without therapy to teach them to interrogate their thoughts to determine if they have negative feedback cycles, how nice would it be to just say "Oh we detect that you are a ruminator, you should do CBT and we'll prop you up with some SSRI in the meantime." The same way we'd just do a Vitamin D or Iron deficiency check.