Well, one of the few if not only major empirical examples we have, Portugal, suggests that if you handle drugs as a social and medical issue rather than a criminal one, you wind up with fewer problems with addiction. And your policing and incarceration costs drop dramatically, leaving plenty for healthcare.
The other thing is that a lot of what you hear about messed-up druggies is either overblown for propaganda purposes, worst-cases held up as cautionary examples, or consequences of the illegal nature of the business (gang violence, adulterated drugs, spread of HIV and hep C, etc.).
It is hard to get one's head around the notion of legalizing "hard" drugs, but ultimately there is far more harm being done by over-the-top drug enforcement, massive incarceration, etc. than consenting adults could ever do to themselves once given access to whatever recreational substances they may want.