So you're saying that a high minimum wage prevents homeless people from getting jobs? That opinion seems overly simplistic -- I'm inclined to believe homelessness isn't a result of the lack of opportunity.
High minimum wage reduces opportunity for those capable of working to find work. And if you are going to hire someone at $15/hr it may mean you now longer have to take a chance on someone less skilled, less experienced, or with a sketchy record. It is simplistic, or simple economics. But of course you are right, the core problem of homelessness isn't lack of opportunity, or lack of housing.
Minimum wages also correlate with higher economic growth, as higher wages mean more people can buy more stuff, and so more people are employed to sell those people that stuff.
Also you leave out mental illness and addiction which are impossible-to-ignore factors when comparing homelessness to impoverishment.