Well, what did stoners do when pot was illegal in the 1970's?
Prohibition was passed with a great deal of political pressure applied by the Temperance groups against a very disorganized opposition. But it was not actually passed with huge popular support: most of the people in the US did not have a drinking problem, many saw no problem with social drinking, and so there was almost immediately what the police today would call "massive non-compliance", and drinkers could access alcohol in many ways, whether from bootleggers bringing it in from Canada or from friends making beer in their basements.
Actually, Prohibition made alcoholism worse. Being intoxicated in public in the 19th c. ( and 18th) was considered shameful, especially during the daytime. Prohibition made it somewhat fashionable, and drunks were considered lovable, funny, - the comic drunk became a stock theater character ( watch one of the Thin Man films) and humorous writers ( like P.G Wodehouse) would feature anecdotes about them. Also, alcoholism had previously been a male problem: respectable women did not go into saloons, and feminist groups had been leaders in the Temperance movements, seeing saloons as threats to families. Prohibition changed that: women were welcome in speakeasies, and would be seen drinking at parties just like the men. As a result, Prohibition really created the whole new problem of female alcoholism.
But you could say that the great increase in drinking also helped to raise the question as to whether alcoholism was just moral failure, as too many different kinds of people were obviously falling victim to it. Someone appearing drunk in public in 1880 would be simply thought morally reprehensible. In 1930, they would be thought amusing. By the 1960's, they would be thought, more and more, as having a medical problem that needed treatment. By making it less shameful to be an alcoholic, Prohibition allowed people to think about more effective ways to treat alcoholism.