Although popular opinion believes that Prohibition failed, it succeeded in cutting overall alcohol consumption in halfduring the 1920s, and consumption remained below pre-Prohibition levels until the 1940s, suggesting that Prohibition did socialize a significant proportion of the population in temperate habits, at least temporarily. Some researchers contend that its political failure is attributable more to a changing historical context than to characteristics of the law itself. Criticism remains that Prohibition led to unintended consequences such as the growth of urban crime organizations.

-Wiki: prohibition

How did prohibition ever gain enough popular support to become law?

2) Because of the Woman's Suffrage movement, as married women and children were one of the people most heavily affected by drunkenness (i.e. husbands drinking away all the money, spousal/child abuse under the influence, etc). Prohibition has great popular support amongst the women of America. And as women's political rights increased, so did the power of the prohibitionists. In fact, one of the Suffragette's main arguments was that it allowed women to escape drunken husbands.

3) The alcohol trade was heavily involved in governmental corruption scandals (in part because they tried to fight the prohibitionists), and so reform-minded progressives (who were in favor of increasing governmental regulation and oversight) increasingly allied with the prohibitionists against a common enemy.

-Eli5: reddit

Regarding (3), it would seem there is a sense in which alcohol was already mafia bootlegged pre-mafia, they just stopped doing it in cahoots with the government!