This is a tautology. You are essentially defining the word "help" as whatever homeless people define help to be, yet you give some credence to the fact that homeless people might not actually know what is actually helpful for them. What is good for homeless people that are on drugs, that don't want to go to a homeless shelter, that don't want psychiatric help are very often bad for everyone else around them. So maybe we should stop making decisions that put the liberties of homeless people first.
In NYC where I live, two Asian women were killed by black, homeless men in this past month. I'm frankly not interested in making my language any more flowery for your taste with homeless people. I'm only interested in real policy solutions. Until you actually acknowledge the violence, the degeneration of our subway, streets, and city, then we're not going to be able to talk any further.
Yes yes people don't always know what they need it can be complex. But the majority of homeless people I know and have known needed and wanted help, but were unable to accept the terms of the help offered by the state, or various charities.
I have been homeless and not some cute "living in my car for six months after college" but open sores untreated addiction rotting teeth in the subway station homeless. People I love are still out there dying those deaths and it hurts so so much to hear the way you talk about them in comments today. Not just this one either.
"These people" need anything but more carceral violence directed at them. I've spent time both in jail and institutionalized. Jail is worse but the difference is more a matter of degree than type.
What you want is to have them removed. You're entitled to your wants of course and even to pursue them. But don't use helping homeless people as part of your justification. It is very hard to read these comments and believe you have ever known or cared about someone who was homeless in your city.