I'm sure there's no easy solution - your way avoids ballooning costs at least. Ideally you'd want to be humane enough so that people avoid frostbite/incapacity, but keep it unpleasant enough to avoid complacency.
Opiate addiction is clearly something that will keep people from lifting themselves out of homelessness: perhaps there's some way to more directly prevent drug use. Regular drug tests with consequences for those that fail?
Ideally their family should bear that burden. If their family is not in a position to do so, or they do not want to be involved, charity can step in.
When the state gets involved things cost more and there is less accountability on the system and the people who are in the program. Drug testing them would just be an additional expense.
A charity and business partnership which allowed people to work for treatment, room, and board would be a system that may make sense.
I can't support any state run program which takes money from those who earn it to provide for those that don't.
"Earning" money is not a simple concept. I'd say there's a lot of money out there that should be taken from those who really haven't earned it, and used for those in need for the benefit of society as a whole.
I would not offer them any assistance. If individuals want to reach out and help that is their business, but the government should not be involved in providing shelters or treatment for them.