It's not just addiction, though that always plays a part. For many it's also about trust. I may be reaching as my knowledge is mostly for here in the U.S., though lack of trust in institutions is a learned reaction. They do not accept help because it has ended badly in the past, and badly may have been as simple as given some hope and had it swept out from under them.
I support aiding homelessness not through the creation of programs alone. Those programs should also come with trained specialists willing to work over time to gain the trust of these people. Who act as mobile case workers and intake personnel into these programs, and keep tabs throughout the process. Now I am sure some personnel exist, and perhaps it is being done this exact way. If it isn't though, some changes should be made. Elimination is unlikely, though there is a huge difference between perfection and incompetence.