None of this nonsense used to happen when
1. People who were too sick to care for themselves or who were too aggressive to be at large could be treated and/or institutionalized even if they refused.
2. Criminals served sentences where they worked, even if it was making license plates or pounding big rocks into little rocks. They usually went into supervised work situations when released.
3. Drugs were not an accepted part of life.
4. Begging and loitering were against the law, not a form of free speech.
5. Living in parks and public rights of way was not permitted.
The homeless here are not described by your statistics. The population that I see every day are drug addicts, alcoholics, thieves and severely mentally ill folks, most of whom (if they are functional) make every excuse in the world for how they got to where they are. Coddling, excuses and appeasement are not the solution. Tough love is. Make treatment and some kind of productive work available, don't allow begging on the streets, no public drunkenness or drug use, and no money or bed if you don't cooperate. Too sick to function? The streets are not the answer for that either.
Everyone's life would be less shitty and uncomfortable, including the homeless, if you actually solved the problem. All government intervention has done is sustain and grow the homeless population. Make the ecosystem less friendly to the behaviors, and you will have a lot less of them.