"As I said, I was being descriptive, not proscriptive. Obviously in a civilized society, everyone has access to a bathroom."I don't know which civilized society you were describing, but it's not San Francisco.
I would agree that that would be ideal, though.
"Also obviously in a civilized society, people use the facilities provided and clean up after themselves. Those that are incapable or unwilling to do this either go into drug treatment, get mental healthcare, or if they are unwilling to do either of these and insist on being a public nuisance, they go to jail."
Except society's problems are not solved by sending people to jail. Quite often they just get worse.
First, the punishment of sending someone who shits on a sidewalk to a jail where they are likely to be raped, beaten, or killed is far out of proportion to the crime they've committed. Few would agree that rape or death was an appropriate punishment for shitting on a sidewalk, yet that's precisely what many people send to US jails face. Hopefully you'd agree that in the very civilized society you speak of, spending time in jail for shitting on a sidewalk would have little probability of bodily harm, rape, or death to the perpetrator. But we don't live in that society.
Second, many people who are sent to jail get out worse than they came in. They are more likely to commit crimes, and are often denied job opportunities or places to live because they've been convicted of crimes. Now, that might not matter as much for homeless people, except that if they're ever to have a hope of being integrated back in to society they shouldn't have the extra stigma of having been incarcerated (especially not for something they couldn't help, like simply going to the bathroom when there were no bathrooms around).
Third, it costs a great deal of money to keep someone in jail, the money would be better spent on bathrooms, housing, and mental health care.
"SF is failing to accomplish any of these things despite a gigantic budget."
If there really is plenty of money, it's clearly being misspent. At least we can agree on that, though I have a feeling that if we looked at the details there'd be plenty to disagree about over which money is being misspent, how to spend it, which programs to cut, and which to fund.