It's a cult, so it's not surprising that it attracts some mentally unstable people. I don't recall there being a much higher number of people with severe mental illness, but those people were probably weeded out through disfellowshiping. I knew of one brother that was disfellowshipped, he was hearing voices, they thought he was demonized, it seemed like schizophrenia to me. I also knew a woman who seemed bipolar who was disfellowshipped for adultery.
If you are stalking about milder forms of mental issues like depression, it sure seemed, at least anecdotally, there was a lot. It isn't surprising to me that an organization that demands so much but gives back so little would cause a lot of depression.
So many things are not really supportive of the individual, like:
High demands on personal time for meetings and field service
An environment that constantly emphasizes the bad in the world
Elders that are not trained in mental health issues, but think they are
A culture that doesnt allow criticism of the hierarchy
Secret judicial committee that harshly judge and punish
Lack of personal choice in dress and grooming
An environment that discourages higher education and setting personal career goals
Entertainment and recreation are frowned upon
Women are demeaned and given no responsibilities in the congregation
Children made to sit through hours of boring meetings every week
Congregations offer little social support, people gossip and have cliques
People are judged and "marked" by others over minor personal choice issues
Families are split apart by disfellowshipping
Friendships are conditional
With all that, the question isn't why are so many depressed, it's why isn't every one.