Well, actually, it was -- in the case of alcohol (I've no idea about opiates and cocaine).
Studies of alcohol use before and after Prohibition shows lower consumption (in a bigger population) and a rotation in favored drinks. Rum almost disappeared, wine almost disappeared, beer came to the fore. And average consumption was down significantly, and it has never recovered.
The 20% rate of alcoholism in France from habituation through social use also argues the same point. Unbridled use leads to higher incidence of habituation and addiction. And alcohol isn't nearly as addictive as what is in the street pharmacy of today.
I also thought there was a trend away from beer and toward hard liquor. At any rate, here are the opiate and cocaine figures from the USDOJ website:
"By 1900, about one American in 200 was either a cocaine or opium addict."
--http://www.usdoj.gov/dea/demand/speakout/06so.htm
That is 0.5% of the population. Fast forward 100 years:
"There were an estimated 980,000 hardcore heroin addicts in the United States in 1999, 50 percent more than the estimated 630,000 hardcore addicts in 1992."
--http://www.usdoj.gov/ndic/pubs07/794/heroin.htm
"The demand for both powdered and crack cocaine in the United States is high. Among those using cocaine in the United States during 2000, 3.6 million were hardcore users who spent more than $36 billion on the drug in that year."
--http://www.usdoj.gov/ndic/pubs07/794/cocaine.htm
Adding the two figures for 2000 together, it works out to over 4 million hardcore users. Using a population figure of 280,000,000, you get about 1.5%, or triple the 1900 estimate on the DOJ website.
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Iran and Singapore had higher rates of heroin addiction than the Netherlands according to the latest figures I found, so I think any claim that tough laws curb addiction are shaky at best.