You have to remember - drugs induce a chemical reaction that occurs inside your body which helps to create an addiction. This isn't like us deciding whether or not to have a second slice of cake for dessert, or postponing a $5k 3D TV purchase.
If we did open up such 'centers' to try and reduce the profits from the drug cartels, it would only create an onslaught of people wanting free drugs. And then, you're assuming the cartels will simply vanish. Many cartels are already 'diversified' in human trafficking/prostitution, and other unsavory activities. Just like other mafia and organizations have 'diversified' into other illegal activities over the years to maintain power and money.
But even if your assumption is correct about the cartels going away when the money flow stops...why won't the cartels suddenly spring back up as soon as the free gov't drug clinics close? There will still be people wanting to get that high from the drugs, and if the gov't doesn't offer the free drugs, they'll be willing to pay for an alternate source (the drug dealer that is now back in business).