I post this with some trepidation as what I am going to say runs counter to many other opinions but is 'how I see it' after a lifetime of coping with a DM and MIL with mental health problems and suffering Clinical depression myself.
Firstly, I believe the answer to the question of why folks are OK to talk about and empathise with those with physical illnesses but not those with mental health problems is that if you, yourself are a sufferer or living daily with someone else who has this problem, then you cannot, for the sake of your own sanity, afford to take on board, or become involved with someone else's problems.
Whilst, say amputees or blind people can gain enormous support and companionship from meeting up with people in the same boat, this is not true for those whose mental health is fragile and can be easily tipped over by becoming too concerned/involved with others in the same boat.
I observed this in a self directed support group for women with depression who met fortnightly in our office's meeting room. They used to arrive bright and chirpy, but no matter what the theme or topic for the session - anything from having their nails done, through relaxation exercises, every session degenerated into an exchange of sad stories, almost a competition of 'my experience is worse than yours' until they went their separate ways miserable and depressed. There was also an underlying ethos of 'It is the medication that causes the problems, come off it and you'll feel much better, like your old self.'
When I saw a wonderful Clinical Psychologist, who treated me as a sentient human being rather than a 'patient' he explained many things. He told me that a person with a mental health problem is not the best person or in the best position at that time to judge whether medication is appropriate or not. He deplored the tendency of the media to report scare stories rather than give prominence to the many positive improvements in medication and therapy. He repeated the mantra that I learned as a trainee Counsellor that counselling cannot work if the person cannot, for whatever reason, fully engage with the Counsellor. Therefore, a period on medication to get the patient on an even keel was usually necessary before they could benefit from counselling.
He also made the point that it is easier, in terms of self esteem, to blame the treatment or medication for your woes or failure to improve, than to accept that you have an on-going illness or condition, which many still consider to be shameful or due to weakness or inability to 'pull yourself together'.
Finally, my recent experience of 'living with (DH's) Dementia' which is also a Mental Health illness has highlighted that people have a very different perception of dementia than other mental health problems. Everyone seems to accept that Dementia can affect anyone, including the 'brightest and best' and that it is caused by physical changes in the brain which have nothing to do with the sufferer's character, or life style. I wish there was the same acceptance of the causes of other mental health conditions/illnesses. On the bright side, whereas the progress of Dementia can be slowed it is, currently, incurable, many other Mental Health problems can be successfully alleviated or completely cured by modern medicine.