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.

Yes, that is a fact. Minimum wage increases unemployment. Ispso facto.

No job ---> no self-reliance.

Homelessness is only a short leap from that point.

Simple does not imply over simplification.

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.