Was Prohibition a failure, since police both failed to enforce Prohibition and through corruption, actually encouraged anti-Prohibition activities?
The results of Prohibition were mixed.
Alcohol had been an issue in the United States going back to colonial days. During the early republic, one of the first crises facing the nation was the Whiskey Rebellion, when farmers who made excess grains into alcohol refused to pay the excise taxes on the product.
Prohibition of alcohol had been a crusade since the 1830s, pushed by health advocates as well as religious leaders. In many places water wasn't safe to drink, but alcoholic beverages were. Estimates are that between 35 and 60% of the crusaders were women. During World War I, many of the combatant countries had prohibited or restricted sales of alcohol so that they could preserve resources for the war effort. The precedent had been set for the prohibition of alcohol sales during peacetime.
People believed that prohibiting the sale of alcohol would result in strengthened moral fiber, as well as a reduction in alcoholism, drug abuse, and related crimes such as domestic violence, street fights, and chronic unemployment. For reformers, the saloons were a vital part of the political machines that drove government in many places. Drinking declined sharply during and after Prohibition; in 1910, per capita consumption of alcohol by Americans was 2.6 gallons per year. In 1934, it was 0.94 gallons. Even as late as 1940 alcohol consumption was 1.56 gallons.
At the same time, Prohibition increased the crime rate, although barely any effort was made to enforce the law. Congress appropriated $7 million dollars for the Prohibition Bureau when $300 million had been requested. There were large areas of the country with no policing at all. As a result, gangs which started in the bootlegging trade quickly became rich enough to expand into "business" with trade unions and other legitimate businesses to expand into gambling or drug enterprises.
Excellent further information (and the statistics quoted above) is from the book "I Love Paul Revere, Whether He Rode or Not" by Richard Shenkman.