Homelessness as "a problem to deal with" means society is selfish, means exactly what you wrote.
A society where people refuse to see it as a social issue, like sickness, and one that requires a lot of thought because you have to remove them from the eyes of people but don't want to deal with the consequences because it's actually a cleanse under a different name (decency, decorum, etc.).
If SF is the least selfish on the planet (which it isn't, unless you consider a few American cities the World), why people refuse to live with what is obviously a byproduct of their lifestyle?
You can't have all the advantages without any of the drawbacks.
Thinking that it is indeed possible is a symptom of a selfish society.
I live near the Colosseum in Rome and there are homeless living here, in the city centre. Some of them have been living here more than I've been alive.
Nobody thinks they are a problem or have to accept the help, people here accept that where there are people with a lot of money there are gonna be desperate people as well.
Because it's only natural.
And because many have been poor or come from poor families, before being wealthy enough to afford a better life.
It's easier for homeless to find what they need to survive in the big city in the wealthy neighborhood than in the small village in the country in the poor quarter.
They also feel more protected, for obvious reasons (more people with money means more people willing to give, means more wasted food, better illumination, better public services, etc.)
For those in need of medical attention, there is the national healthcare, we call the ambulance, they already know who these people are, bring them in, give them food, a bed and a warm shower and they already know they'll be out on the streets again in a couple of days.
At least they have been checked and their health conditions assessed.
Because it's their job, they don't have to respond to some kind of profit based mechanism, people taxes already paid for it.
Homeless are not treated like a problem, like rejected or defective people, they are taken care of. Because it benefits the society at large.
Of course some of them are a problem, but it's a tiny minority, our biggest issue is finding as many as possible in winter so they don't die in the street for hypothermia or other cold related disease.
Of course is not all roses, we are still talking about people living in the edge of society and sometimes dealing with them is not a pleasant experience, but it's rare.
Also the police here don't treat them like criminals, which is an important difference as well, police usually protect them from bad people. They are in fact much more often victims of violence than perpetrators.
(According to LAPD report in January this year more than one out of three times police officers used force against homeless people in 2019, a 26% increase from 2018)
It's really not that hard, especially for one of the richest cities in the richest country in the World.
Unwillingness is a form of selfishness.
Not learning from what others already do better is a form of entitlement.
Which is a form of selfishness.