You give them a home. Then they are no longer homeless.

The fact that this is also demonstrably (in several different jurisdictions now) less costly than either imprisoning them or dealing with the other consequences of a significant homeless population should make it a no-brainer.

But too many people have internalized the idea that no one should ever have anything they haven't "earned", including the basics necessary for survival (food, shelter, clothing, clean water, etc), so there's always angry opposition to this. (Plus, of course, the racism angle, which is fairly significant, if often unspoken.)

With regard to the mechanism of "compensating for the lease of the part of our living planet they should be entitled by birth", I think any means tested or regulated approach is problematic. Instead provide to them rent checks for the slice of the world society has taken from them, and provided to others for private ownership / exploitation.

Let a market economy sort the development and allocation of resources.

We've already run the real life experiments, as suggested above. No need to try to delve into minds and motivation and life goals and other such nonsense (nonsense not in the sense that it's not true, but nonsense in that it doesn't bring any helpful ideas to the policy decisions that should be made.)

Drug addiction and the development of open drug spaces is not just a symptom of homelessness. If you solved housing and it became a human right, you would probably reduce the development of open drug spaces, but it certainly wouldn't be eliminated.