On one end of the spectrum, temporary homelessness typically garners the most sympathy, and brings the least trouble in terms of drug use and other petty crime.
On the other end, the chronic homeless are harder to deal with. My ex who worked with the local metro homeless population was frustrated by these, who through mental illness and / or drug use were simply not capable of dealing with the responsibilities needed to maintain a home or apartment; things like getting a job and not getting evicted for various bad behavior reasons. The hardest to deal with were those who refused to get help; no medicine, no job training program, no finance management couse, nothing accepted but food and cash.
These are the ones who are often the most visible- defecating on sidewalks, drugs, harassing people who are just going about their day.
You can have the biggest heart in the world, and you still won't be able to help them short of bringing back forced institutionalization, which no one wants either.
People who recently have become homeless would qualify, assuming they could provide mail or something from a year ago, but even that seems like a stretch for most people, I think.
Also, I don't know about SF, bit quite a few of the services provided here in the Midwest are privately run (I.e. in association with churches or otherwise non-profit), and I don't know that such a ban could be imposed on them.
They also aren't necessarily liberal when it comes to their personal safety.
Once you realize that the vast majority of the bay area is there to maximize their own financial advantage, not to change the world, the bay area makes a lot more sense.
People are individuals--watch what each individual does.