The thing is at that point its no longer psychiatry, such issues would automatically fall under the domain of another discipline. You are trying to redefine "good faith belief systems". Science is science and follows the scientific method, religion is religion.
Thats why we still have psychiatry, thats the way the high priests of psychiatry like it.
I do have a prediction that psychiatry might go the way of the dodo, it might easily be split into psychology (the psychosocial coping stuff) and neurology (biopharmacy). Not all psychiatry is pseudoscience though, just a lot of it. It might be as much as 90% though.
Some of the biopsychiatry has some foundation, though not perfect.
Freudian psychiatry was like a cult, and so are many specific forms of psychopsychiatry, which are based on the received wisdom of supposed enlightened psychiatrists. Talk to a Jungian, for example. Webster makes a good case as to why this is very much like religion.
There has also been a tendency to have diseases peel off and go into other disciplines, and while I have not kept up with research I suspect schizophrenia might wind up as immunoneurology. Depression is of course from many different causes, including infections and metabolic or dietary issues. Its a cluster of similar symptoms, and not a valid diagnostic category.
Yet there are instances of biopsychiatry such as with depression subgroups, where they respond very well to antidepressants. Where it goes off course is how that is generalised to all depressive symptoms. The theory is mostly bogus, but some science has been successfully applied ... so what do you call that? The serotonin deficiency hypothesis is almost all from marketing push from pharma. That isn't religion. That is capitalism gone amok. The religion of capitalism? I would argue its more an ideology, though I am not sure where ideology ends and religion begins.
I personally want to see most of psychiatry be moved out of medicine into alternative medicine. I would like to see the entire psychiatric evidence based movement, including in Cochrane, put under intense scrutiny.
I would like to say the issues are all in psychopsychiatry, but sadly I don't think that is right either. Most of psychiatry is caught up in category errors.
So where I think psychiatry might have a future, if it does, is as some form of psychoneurology. Sadly I see it hanging on as the Science of the Gaps, for quite a while yet.