American military personnel drank alcohol when off duty in WW1, WW2, Korea & Vietnam to no discernable negative impact.
You can't be serious.
When I read this, I thought immediately about this story I watched on the 5:30 evening news.
I also specifically remember being in a GI bar in Stuttgart in the summer of 1976. Weed and beer were the least of it.
To quote yourself, "Weed and beer were the least of it." So why prohibit either?
The US (and its erstwhile allies, including a vodka-soaked Red Army & a not-too sober British Empire) conquered Germany, Italy & Japan in WW2, all the while having official "rations" of alcohol for our armed forces, i.e. liquor for officers, beer for enlisted men.
The morale problems in the US military in the Vietnam War were less related to drug-and-alcohol abuse than they were to the war itself. The video clip you referenced (I think it was from CBS News "A Day In The Life Of Charlie Company" from 1970-1971) was late in the war, when America, and its troops, were sick of the war.
Compare this to WW1, for example, when consumption of alcohol was prohibited for US troops (by America's puritanical society) in France. Our doughboys completely, totally ignored this regulation while imbibing vast amounts of French wine and beating the hell out of the Germans at the same time.
American troops marched across Europe in WW2 armed with M1 rifles and contraband Italian, French and German wines, beer and liquor. Remove the booze and morale would have suffered substantially. Same with GIs access to prostitutes - let's be honest. In the Pacific, officers conveniently overlooked GIs and Marines home-made stills made out of whatever was handy. This didn't stop the conquest of Saipan, Iwo Jima or Okinawa one bit.
Frankly, I don't think there has been an army in history that hasn't used (or tolerated) booze as a weapon in it's arsenal (OK, maybe ISIS).