I'll like to clarify that you are forgetting some states of India, where Prohibition has been in effect for over 50 years. Leaving aside the recent prohibition in Bihar & kerala (Because of 20 year rule), Several states such as Gujarat, Bombay Province, Andhra Pradesh, Tamil Nadu, Haryana have had prohibition at one time or other.

In Most of these places, the justification has been a Gandhian Perspective, where Alcohol has been seen as a Social Evil. Infact the founding fathers even put Alcohol prohibition as a Constitutional Objective in the Article 47, which is a part of the Directive Principles of the Indian Constitution.

I can only speak for the US and (to a far lesser extent) Canada, but you have to understand what a legitimate problem alcoholism was "back in the day." People, on average, drank far more than they do now, and addiction wasn't as well understood. "Temperance" (the name is rooted in simply encouraging people to drink less and possibly swear off hard liquor, but came to be a euphemism for prohibitionism) gained steam throughout the 19th century, becoming one of the leading issues of the day. So, by the time Prohibition was ratified the movement had actually been around for nearly a century. As time went on, it also morphed into a convenient scapegoat for a wide range of issues by an equally wide range of people.^1 You get the sense these people truly believed that if they simply ban alcohol, the world would transmogrify into an earthly paradise, even if many of their utopian visions were mutually exclusive with one another. As to how it ended so quickly, it didn't take long for people to realize that laws banning something so easy to make that was desired by so many people could never be meaningfully enforced. It took root as a cautionary tale in the public consciousness- just look at how often it comes up in modern discussions about drug legalization. I guess this is technically speculation, but it would be very difficult to argue that Prohibition's undeniable failure didn't doom attempts to bring it back, especially since many leaders in the Repeal movement like Pauline Sabin and Pierre S. DuPont had started out as temperance supporters. It didn't vanish overnight, though- Temperance sentiment waned throughout the 30's and had basically disappeared at the mainstream, national level by the end of WWII, but organizations like the Prohibition Party continue to exist to this day. So ultimately, it wasn't purely a 1920's phenomenon, that was simply the peak of their power and influence.

Also, while those were the only countries where such bans were passed (and I'm sorry, since I can't give an overarching reason why it was those countries specifically which is what you were really asking), the Temperance Movement was quite international by the standards of the time. These groups existed throughout the Western world and their leaders would correspond with one another. Britain had an active, if ultimately ineffectual, one while France's was partly responsible for the banning of absinthe.

^1 : I made this into a footnote because this part was a bit of a tangent and getting too long, but it's important to realize how diverse the coalition that brought about the 18th Amendment was. Feminism and temperance were famously intertwined, as it was a way to discuss issues like child abuse and marital rape, as well as a way of empowering women to demand suffrage who would otherwise find taking part in politics unseemly, but seemingly everyone (by which I mean, everyone who was a white, rural, native born, Anglo-Saxon protestant along with a diverse smattering of others) had a reason to want to ban the bottle. The Ku Klux Klan were major supporters, as a weapon against blacks and "white ethnic" immigrants, but so was civil rights leader Booker T. Washington and many progressives who specifically wanted it to improve the lives of those immigrants. Many socialists saw alcohol as part of a plot to keep working class dumb and distracted at the same time as leading industrialists like Henry Ford were promoting it to make their factories more productive.

Source: Daniel Okrent, Last Call: The Rise and Fall of Prohibition