(I live a few blocks from the worst areas and see people dealing drugs and shooting up every day)
Physical illness and drug addiction (and even mental illness in some cases) are more likely a symptom of homelessness than a cause.
From accounts I've heard from homeless people, one of the biggest problems homeless people have is boredom. This leads to both depression and drug use, both of which can lead to both physical and mental illness.
The OP seems to be discussing the problem of solving it in a global sense, so that people do not become homeless. IMO, more housing is the solution to that problem.
The GP seems to be discussing the problem of solving it in terms of the existing homeless population, which, regardless of causation or the directionality of any causation, does require dealing with the mental illness and drug abuse issues.
IMO, it's not, because people don't become homeless (for the most part) because there are no existing vacant housing units, they become homeless because of joblessness, poor credit, drug addiction, mental illness, and criminal issues (often involving drugs), or a combination thereof, which make them unable (financially or otherwise) to either rent housing in the open market or take advantage of publicly operated or subsidized housing.
> ... which make them unable (financially or otherwise) to either rent housing in the open market or take advantage of publicly operated or subsidized housing.
This is made easier when there is more housing available.
Being physically ill isn't a correlation of having neither money nor a home. /s
Being addicted to drugs isn't a symptom of mentally checking out to avoid the problems you're literally unable to address. /s
Edit: yes, you're right, it's a lot more complicated than just housing. But housing, I think, is a big cause.
The difference can be illustrated by looking at how a measure meant to solve the latter, creates the former.
Suppose that we mandate that all housing created needs to be reviewed and a certain fraction of that housing needs to be set aside for affordable housing. You will indeed increase the amount of housing available at the price point that you have deemed affordable.
However the same action is a disincentive to build new housing, and also artificially reduces the supply of housing being sold at what would otherwise be a fair market price. This measure restricts supply, and in accord with economics 101 will increase average prices.
The result? More affordable housing AND a higher average price of housing. The net cost of housing goes up. (Which ironically will tend to cause more people who were on the edge of being able to afford housing to become homeless, making it likely that they lose their jobs, and thereby creating more need for affordable housing. Aren't you glad that we're doing something about the affordable housing problem to help them?)