your first source says verbatim: "One of the main causes of homelessness is the lack of affordable housing". it also doesn't link addiction or mental illness as a cause - it describes that the rates are higher in unhoused populations
a brief thought experiment: if you were unhoused, living on the streets, barely enough money for food and water, your body exposed to the weather, knowing that society looks down on you at worst or ignores you at best, how would your mental health fare?
well, according to your second source:
> It can be more challenging for people who are homeless to stop using substances, because they may not have easy access to treatment, often have smaller social support networks, may have decreased motivation to quit drugs or alcohol, and may have other, higher priorities, such as finding housing or food
it's almost like being unhoused itself causes cycles of addiction because at least the drugs take the pain away for a short stint?
your third source similarly contradicts your initial claim:
>For years, ending chronic homelessness was thought to be a multi-step process, with individuals receiving treatment for addictions and illnesses, perhaps while living in transitional or temporary housing, before being found capable of living on their own. However, the strategy for ending homelessness has changed, largely due to research pioneered by housing providers. Instead of requiring chronically homeless individuals to be "housing ready" by first addressing issues thought to underlie homelessness, the new strategy allows chronically homeless individuals to move into permanent supportive housing without preconditions.
either find better sources or actually read the research you're citing, learn from them, and stop making unfounded and ludicrous claims you can't even back up