I grew up poor but from a generally stable family and through both my own poor decisions and some circumstances outside of my control I ended up homeless. I never suffered from addiction or mental health issues and I still ended up on the streets, so I can sympathize with how hard it must be to tackle those issues simultaneously.
I'll agree with you that we should do much more to tackle these issues early on before they turn into more chronic problems later in life. The initial cost would be expensive but it wouldn't surprise me if it ended up being cheaper in the long run.