We see several of Dr. Crusher's staff over time, but we see no evidence that Counselor Troi oversees any kind of staff.
Also, didn't they establish in TOS (Whom Gods Destroy) that mental illness had basically been cured? I'm not sure I buy that, since there are so many forms of mental illness and I think TOS simplified it too much. But the idea presented was that there was very little mental illness in the universe since the brain was completely understood.
This would leave a psychologist with much less to do, other than handling day to day family issues, as well as the occasional immediate traumatic situation.
I would like to think that the stigma against mental illness and therapists in general would be gone by the 24th century, and hopefully long before.