Caffeine as a drug would also probably be illegal, so coffee would have to have the caffeine removed and just be an awful tasting drink that no-one would buy. More likely coffee would simply be completely illegal as it would be hard to verify it has been decaffeinated.
If so there might be a worldwide productivity drop.
OOC I assumed that Alkohol Prohibition happened as OTL. If not the case please PM me and I will delete/edit it out
No coffee? What kind of dystopian universe you are talking about?
I don't think that coffee would be banned, it is simply too common. And if you try to prohibit something as common as use of caffeine, where would you end? The answer is in Orwellian 1984 - with alcohol banned alongside with sex. (both alter the brain activity).
Now, seriously.
Considering some reasonable prohibition on drugs lets say mentioned cocaine, meth, marijuana and psychoactives, either in XX or XXI, one has to understand that this is big business. The pharmaceutical industry in US would either go bankrupt or go abroad. Like during the Alcohol prohibition, you would see a line of ships offering "double trips" outside territorial waters, and drug shops alongside Canadian, and Mexican border. Borders would be rife with smugglers. This wouldn't be a nice friendly border, where you pass freely, just waving your passport to customs officer. Oh no... You would have concrete fortifications, barbed wire, aerial and land patrols, car and personal searches. This would be a constant state of siege, limiting commerce, wasting resources that could go to something… well useful and producing scores of criminals.
More over people would look to work around the law. Methamphetamine is banned, oh no! It is not like there are dozens of similary acting isomers which are only somewhat more toxic and a little harder to do

Just ask anybody with degree remotely related with chemistry.
Even if you somehow legaly prohibit use of all of them, people would start taking prescription’s drugs to get high, just like they got drunk on "medical alcohol" in the twenties
Also, imagine what would happen if certain drugs deemed widely became illegal around the entire world.
Lastly this won't happen. Ok let's say that after II WW USA forces Latin America, war - torn Europe and their colonies to enforce prohibition and actually pays attention that this ban is enforced. Now let's skip to eighties, when Soviets realise that they are almost broke. Or China realises that they need additional income. These are nuclear powers, and no one would want to go to war because of drugs.
Although I must say that a Third Opium war with China pushing the opium to American ports is hilarious prospect.
