The idea is that welfare programs don't help homeless people that much - because without some base of stability (a place to stay) - they are permanently uprooted and can't connect in any meaningful way with civilization.
i.e. try to 'get a job', if you're homeless. Even if you could - how do you get a bank account? A cell phone? Literally just 'take a shower' and 'brush your hair'?
If you have a 'home base' - then you can get a 'footing' into the system.
It works quite well when the other layers of social assistance are there, this approach was validated in Finland.
If you just give a drug addict a home and walk away, then it will not work.
These programs, though, aren't for the people who want to fix their lives and want services -- there are resources out there for people who are willing to, for example, not do drugs or destroy the place or do violence.
If you are homeless because you lost your job and have no money and got evicted (which basically doesn't happen in San Francisco anyway with the eviction moratorium), you can get help. You can find a shelter and food and basic services to give you the stability required to start rebuilding.
Those resources rarely fill up, because most of the homeless people still on the street aren't willing to obey the rules of those places.
The "Housing First" places are specifically housing that doesn't require you to care about putting down the drugs or stopping destroying stuff or caring about having a better future.
'Housing First' literally implies a 'Second' and 'Third' issue to be addressed.