SF actually sort of attempts to do that, and spends more than enough money to do that, but is ineffective to the point where the homeless are either disincented to participate, or are stuck in a weird limbo where the city/state/fed/charity give them enough to survive indefinitely, but not to actually improve.

In fairness, well over half of the SF homeless population are mentally ill or drug addicted, which would probably be covered by other programs elsewhere; some of which (on the mental health front) is missing because the US had a lot of issues with horribly run institutions until the 1970s, so they shut most of them down, but didn't provide an alternative.