There are two battling narratives of mental illness. The first narrative says that mental illness is a disease of the mind, the second that it is a disease of the brain.
The "mind" story is that these illnesses come from bad ways of thinking, whether this be childhood trauma, diseased patterns of thoughts, etc. The treatment is therefore in psychotherapy, CBT, or other such. To the extent that this narrative is true, discussion of mental illness is likely relevant to rationality.
However, the other narrative is that mental illnesses come from chemical imbalances or other defects in the brain. The cure is therefore lithium, SNRIs, etc. To the extent that this narrative is true, rationality doesn't have a lot to say about mental illness.
Your post suggests you like the "mind" narrative. But to the extent that LW is a hive of reductionism, it may be that the "brain" story is considered more appealing here, and this may explain why there is less discussion of mental illness than you find conducive.
To the extent that LW is a hive of reductionism, we believe that the mind is the brain, and psychotherapy and medicine can both be used to treat its diseases.
For a site extremely focused on fixing bad thinking patterns, I've noticed a bizarre lack of discussion here. Considering the high correlation between intelligence and mental illness, you'd think it would be a bigger topic.
I personally suffer from Generalized Anxiety Disorder and a very tame panic disorder. Most of this is focused on financial and academic things, but I will also get panicky about social interaction, responsibilities, and things that happened in the past that seriously shouldn't bother me. I have an almost amusing response to anxiety that is basically my brain panicking and telling me to go hide under my desk.
I know lukeprog and Alicorn managed to fight off a good deal of their issues in this area and wrote up how, but I don't think enough has been done. They mostly dealt with depression. What about rational schizophrenics and phobics and bipolar people? It's difficult to find anxiety advice that goes beyond "do yoga while watching the sunrise!" Pop psych isn't very helpful. I think LessWrong could be. What's mental illness but a wrongness in the head?
Mental illness seems to be worse to intelligent people than your typical biases, honestly. Hiding under my desk is even less useful than, say, appealing to authority during an argument. At least the latter has the potential to be useful. I know it's limiting me, and starting cycles of avoidance, and so much more. And my mental illness isn't even that bad! Trying to be rational and successful when schizophrenic sounds like a Sisyphusian nightmare.
I'm not fighting my difficulties nearly well enough to feel qualified to author my own posts. Hearing from people who are managing is more likely to help. If nothing else, maybe a Rational Support Group would be a lot of fun.