They do. But the people on the street would have trouble affording rent anywhere in the nation. SF has a very mild climate, and lots of social services, so it’s relatively better than other places to live outside. Like, why be homeless in low rent Houston when you can easily hop a bus to LA, SF, or Seattle?
Yes, but for the vast majority that don't want to remain homeless, even if you give them free housing and they find jobs, they still can't afford an apartment in california. Are they supposed to move back to "houston" and find another job? No way! So how can they escape homelessness? Some might hustle their way into actually affording a place in cali but that takes a lot of will power and overcoming a lot of things that can have them back on the streets.
Meanwhile, there are many people in cali that get free housing but are stuck as meth addicts or something because why not? And a lot of people born in cali also lose their housing status. If it was realistic to get housing by simply finding a job and working hard, free housing can be made to work, but that isn't reality unless you make six figures. Look at rental ads in LA, I was shocked to see what is the price of an expensive apartment in most other cities, in LA that gets you a bed, not even a room, just a bed.
We’ve been relying on supply and demand economic signals to decide who gets to live where they want. I don’t see a huge problem with that, there are plenty of de-populating areas in the Deep South and Midwest that could use more people.
You want to live housed in LA? Then pay the living in LA tax. At least you can crash with your parents if you are local. But the greyhound bus terminal has tons of people just showing up everyday who think they can make it but haven’t thought things through very well.
Houston has plenty of jobs and a bit cheaper rent. But many unhoused are unable to afford housing anywhere so it’s not useful to talk about just moving them to where rents are cheaper. They also lose the social services that rich cities can afford via their tax base. You would have to be deft to not move to California (or another rich city with mild weather) if you were homeless, I totally would do it so can empathize at least.