A homeless person wanting to live only in SF is just like a starving person wanting only caviar; it's a luxury good that they're not going to realistically get because so many others want it as well.
If you want better availability of infrastructure, better opportunities to make connections, and a better quality of life, then the question is how to improve the quality of life at locations which currently have low cost real estate - and decoupling income from jobs is one way that can happen; for many of these places the living environment actually is quite good (mainly because you can afford much more space), but the main (only?) problem is the lack of local jobs; if the local people wouldn't be forced to move to where the jobs are, there's nothing wrong with the infrastructure.
Homeless people gravitate towards big cities because that's where the concentration of services tend to be. It is why I went to San Diego: there are enough soup kitchens there to eat every day, even if you have no money or benefits at all. I left San Diego after I got food stamps and had dealt with a few things where I felt I could cope without daily access to homeless services.
It's inhumane to suggest shipping people elsewhere and actively evicting them from a particular city because they are poor. This is a mentality similar to the one that was behind removing Native kids from their families, sending them to boarding schools, forbidding them from speaking their own language, etc.
I have a collection of websites I run. I actively encourage people to do things like develop portable income and move someplace cheaper. That is exactly how I got back into housing.
But one woman I spoke with couldn't move because she was currently a college student. She had huge student loans that would immediately come due if she dropped out of her program. She needed to complete her degree in order to have any hope of making her life work.
Other people have children and shared custody with the other parent, or they can't leave because they are on parole and are required to remain in the area or any number of other reasons.
Homeless people are still people. They still have many things going on in their lives that can give them ties to a particular place.
Homelessness arises out of complex, multifaceted problems. One-size-fits-all solutions do not work and tend to make things worse, not better.
Yes, but the scarcity of real estate hasn't changed - there haven't been any holes suddenly opening up in the ground and decreasing the amount if available space. Nevertheless, housing prices have skyrocketed (and so have the number of homeless from what I've read).
So to stay in your frame of discussion, it seems the definition of what is "non-luxury" living space has shifted considerably.
It's not just about availability of work, it's also about the availability of infrastructure, opportunities to make connections, in short, ensuring a decent quality if life.
If the current trend continues, this will probably push larger parts of the population to increasingly low-quality living spaces. This isn't even a problem restricted to homelessness.