Canada already has disability benefits, social welfare, OAS + GIS, universal health care. If people are still homeless despite all that, why should we care?
As for mental illness, as ToadBrother said, there's no definition. Show me an abnormal CT of a baby whose mother didn't use alcohol, cigarettes or drugs during pregnancy, then I might have some sympathy.
So the real question is not how should we save money, it should be why we are spending money at all. If it's purely a crime prevention scheme, then I am sure it can be done much cheaper. Toronto spends $800 million/year on social housing alone.