Poor Shakespeare. I sense that he wouldn’t be quite delighted to see his magnificent work used for such profane purpose.
As it is oftenly case with poets and philosophers, mental illness are being poeticised, romanticised, if not demonized, all to illustrate an act of crossing the borders for which only geniuses or fools for Christ (see:
https://en.m.wikipedia.org/wiki/Foolishness_for_Christ) are capable.
So what we have in such works is basically, an anti psychiatric approach - I can see why you choose a fictional charachters and imagined life to get the arguments for real world (sic!)
In the core of anti psychiatric modeling of characters in Shakespeare’s world is a relation described by one of his readers.
"The disease is becoming the answer to what life is and what life gives: disease, seen as escape, as well as freedom from responsibility, unconditioned anything, but the disease is seen as confirmation of identity, as a confirmation of himself in a world where there is no room for any identity or for their own realization that it would not be seen as a “success” or “defeat”. For us, for our culture, the disease is a death because life means absolutely Health; It is for man loss of self because the only identity that arises is the identity of a healthy man, efficient, productive (…) The disease is the fear of the unknown, unfathomable. "
As if our mental health problems have only a physical source!
PS. Not only that your arguments are borrowed from vulgar realism but they also represent a dangerous method sometimes called reversed mimesis - a belief that life imitate what is written in fictional worlds.