You would be mistaken. I'm no expert. But, I've been in SF long enough to talk to many homeless people there and read a bit on the subject.

Paranoia, drug dependence, coping self-delusion, self-destructive pride and sometimes genuine personal need cause a huge number of homeless people to outright refuse housing when offered.

This article had some stats of recent outcomes from offering shelter (and towards the better end of what's available) to displaced encampments: https://www.seattletimes.com/seattle-news/homeless/57-people...

Far from the worst uptake and outcomes, but also far from great.

Depending on the housing situation being offered.