Your error is to conflate "mental illness" with "mental disability". The former is frequently treatable and sufferers can rejoin society as productive members of the community, as in this example (alcoholism being considered a mental illness).
Someone who is mentally disabled, as in unable to take care of themselves, would not be able to survive long-term homelessness.
Ah, ok, another interesting point. The reason why "disability" came out, was because many years ago, I was complaining to a friend about the conduct of beggars in NYC (not the begging part), and I was told before that a significant proportion of the beggars in NYC were mentally disabled.
This is the insanity defense. There are two outcomes of this.
First, insanity defense stands, and they are absolved of responsibility over their actions. I did indeed conflate the two, and it is part of the reason why I thought doing something different may not change the optimality of the current situation. (They have a switch they cannot turn off unless you constantly medicate them (very expensive), and so if the social burden isn't great, do nothing.)
Second, it doesn't stand, then perhaps there is a conclusive economic value and societal benefit in a program that helps reassimilation. But it's not that simple: suggesting it is a non-innate trait implies that there was volition involved in their behavior. Again there are two ways to look at this:
1. they are consciously obstructive and antisocial (technical definition) members of society, which is, in a way, criminal.
2. they have a tendency to lapse into such illness, which comes around to suggest, again, something innate.
To point 1:
If you have a stomach virus, you may find yourself puking all over the floor. Nobody asks "why is he puking all over the floor? Can't he see that's inconsiderate?" At that point, you are unable to help yourself. However, it's clear that if we take you to hospital and get you well again, you will be able to get on with your life.
The problem with mental illness is that it messes with the concept of "intentional" behaviour. If you are mentally ill, your sick brain may motivate you to do something antisocial or even criminal that, were you mentally well, you would never do.
So just because it is intentional _at the time of illness_ doesn't mean it is truly intentional, conscious behaviour.
2. Consider a diabetic. Without regular shots of insulin, they will lapse into a coma. More "criminally" antisocial behaviour? Many forms of diabetes are a combination of genetic and lifestyle factors -- these people have a "tendency to lapse into diabetes", if you will. However, with regular shots of insulin and other lifestyle changes, they can be perfectly productive individuals.
Again, with mental illness it is harder to see that someone with a genetic predisposition to imbalanced levels of, say, serotonin, triggered by drug abuse, is not at fault for their condition. But with medical treatment and lifestyle changes, they too can control their condition.
In both cases, it is in society's interest to help them do so, even from the barest economic principles. Factor in some basic human compassion, and it becomes imperative.
Perfectly reasonable and agreeable, until the last paragraph.
It's hard to quantify because in the other cases, such as diabetes, the effects of insulin and no insulin are quite well determined, as an all-or-none outcome, and the cost-benefit analysis is very straightforward. Not so sure about the case of dealing with the head.
So we may go ahead with some program under the principle of "capable until proven incapable," telling ourselves that there is definite positive benefit. It may well be true, but the payoff is distance and uncertain. Also, is coercion involved? "We will provide free training for you" ... after a few days "screw this I want my alcohol" -- at this point, what to do? Extend the counseling? Or, trust their rationality that they are capable of seeing what is in their interests?
If the current situation is grossly suboptimal at least one person should have been looking for a solution. Misfits have been around for long enough, making me think it is part of the social dynamic. Or, the unpopular question that no politician will want to hear.
Someone who is mentally disabled, as in unable to take care of themselves, would not be able to survive long-term homelessness.