Sorry I don’t mean that 1/3 sleep rough, more that 1/3 have big mental issues (and tend to be the ones that sleep rough and the ones you envision when you hear the word “homeless”). For that cohort housing first makes them not-homeless but is insufficient to address their problems. They’re not able to take care of themselves and would need a lot of labor to keep their place habitable and safe.
You would probably spend much more money on maintenance and cleaning than you would on the structure
The evidence disagrees. Housing-first policies in multiple countries have been a smashing successes in reducing addiction, so clearly there are some factors you're missing. For instance, theft and violence is a huge reason homeless people avoid shelters. Having a sanctuary that's somewhat secure from thieves and muggers means they actually add some stability. Stability makes their lives less shitty which reduces the urges to use to escape their shitty situation. That's just one example I've read about.
You would probably spend much more money on maintenance and cleaning than you would on the structure