Nowhere did I say or imply that homeless people are "inherently" anything, and I never said or implied that a problem "cannot be solved". Quite the opposite, I'll assert that housing-first plus treatment is in fact a permanent solution for many indigent people, and I wholeheartedly support it.
In your apparent lack of experience, you're strawmanning any argument that doesn't align with your opinions.
And you also apparently forgot to read the study you cited, because it supports exactly what I've been saying: fourteen percent of their participants could not be kept in their intensive housing+treatment program. Fourteen percent is a hell of a lot better than the usual two-thirds, but that's still a whole lot of people that we don't know how to help, no matter how many resources we throw at them. I know people just like that, even if you refuse to acknowledge their existence, and I don't pretend to have the answers. It's a hard, hard problem.
How about this: since you seem to have this figured out, write up your proposal for a permanent, humane solution for that fourteen percent. I'm sure the folks who've spent careers trying to figure it out would love to know what you think they're doing wrong. Go get em tiger!