To be honest greencycles, I don't really think that would change the status quo much. The reason for that is places like you described already exist in a way. Methadone, which is another variant of opium, and used as a treatment for heroin addiction (much in the way heroin used to be used for morphine addiction.) And free methadone clinics exist all over the United States funded both federally and at the state level, and also by private insurance and medicare/medicade. I don't have statistics on it, but from my point of view this leads to what we call drug seeking behavior in patients. They will call 911 for an emergency like shortness of breath, but low and behold by the time we reach the emergency room they are breathing perfectly fine and are screaming in pain demanding medication.
There is also an interesting phenomenon that occurs mostly in low income families. They tent not to seek healthcare services, free or not, until it becomes an emergency. They seem to prefer to be processed through an emergency room rather than utilize any kind of preventive care.
It's an interesting though experiment, but I really don't know the answer.