A less drastic but far more humane solution: involuntary incarceration for the "homeless".
Get them into a detox/rehab. Re-educate them to be decent citizens. Then provide supports to keep them off welfare & off the streets.

The severely mentally ill may be held there for life, but I think that's better than living in hell.

Unfortunately the US mental health industry was FAR worse that it's prison system ever was. It took the Quakers in WW2 to unmask the nightmare. Then when pharmaceuticals came along every nation basically closed every asylum :/
So here we all are putting the mentally ill in prison. Or letting them rot on the streets.