> I do not know why doctors are so hesitant to link the immune system and mood disorders.
People who call themselves doctors — e.g. neurologists — generally aren't hesitant to do this. But psychiatrists — and even moreso, therapists — generally are. And psychiatrists+therapists lead the conversation on mood disorders, since that's who everyone is talking to about their mood disorders.
IMHO it's just the hammer-and-nail thing. To a cardiologist, every medical problem is seen through a potentially cardiovascular lens; to an oncologist, every problem is a question of what type of cancer could cause it.
Psychiatrists are technically medical doctors, but they spend their entire careers (after a few short years of school) focusing on psych cases; where these patients' problems either are purely psychological (e.g. conditioned-response, traumatic-response, coping/defensive, attachment-related, etc.), or at best "we don't know" the degree to which they're psychological vs organic. (If we can recognize a problem as purely organic from the outset, that problem doesn't end up in the hands of a psychiatrist!) And either way, they usually see good results in clinical practice from treating the patient's mind, rather than addressing organic signs/symptoms directly. Even when they prescribe medication, they're measuring their success on a mental basis (using questionnaire-based instruments used to gauge mental changes) rather than observing changes in e.g. measurable behavioral signs. The problems they're faced with, and the successes they have via these models, reinforce in psychiatrists a mind-centered mental model / worldview for psychiatric disease. (A model which is "the right one" to use in many psychological diseases! But not for many others.)
And therapists aren't even medical doctors. They never learn much-at-all in school about potential organic causes of psychological (or medical) problems. They focus purely on this lens of "the mind", ignoring the lens of "the brain as an organ" entirely. This means that in clinical practice, when confronted with a problem that has both mental and organic aspects, a therapist will tend to ignore the organic aspects; and when confronted with a problem where the organic aspects are too large to ignore, the therapist will simply refer to a psychiatrist (or neurologist, maybe) — with no follow-up, and thereby, no way to end up learning what the patient's problem actually was and thereby evolving the neurological side of their understanding.