Not necessarily; the fact that alcohol use rose during the last several years of Prohibition shows that there is no ironclad correlation between legal status and level of use. Do you have evidence to support your claim?
But I agree the war on drugs is not fair to responsible citizens. I favor legal access for those already addicted.
Legal access for those already addicted does not address my question: "how is it moral or just to impose all the costs (monetary and otherwise) of the War On Some Drugs on responsible citizens in order to protect irresponsible ones from their own irresponsibility?" That would still place the remaining costs (monetary and otherwise) of the War On Some Drugs on responsible citizens in order to protect irresponsible ones from their own irresponsibility.