You're ignoring mental health and addiction just as much though. Both are complex and interrelated. Poverty is incredibly stressful; my mental health was never as bad as it was when I was homeless.

Harm reduction is effective. I literally got off the street because someone gave me a garage to sleep (and use drugs!) in and $14k. Having a private space meant I stopped getting arrested for using, didn't risk losing all my possessions every time I went to a job interview. Allowed me to think about a future farther than 30 hours away. I could afford (and store) weed and beer instead of vodka and crack. I didn't have to be obliterated to sleep through the cold & noise of the highway under the bridge.

The first small steps were only possible because no one held me to the sort of standard you're advocating for.