"A simple congressional majority could adopt a statute [to ban alcohol]"
Says who?
Are you saying that a simple congressional majority could not adopt a statute to ban alcohol? Where's your proof?
I don't recall an amendment for The Lever Food and Fuel Control Act of August 1917 which banned the production of distilled spirits for the duration of the war.
After the war was over, I don't recall an amendment for The War Prohibition Act of November 1918 which forbade the manufacture and sale of all intoxicating beverages of more than 2.75 percent alcohol content, beer and wine as well as hard liquor, until demobilization was completed.
A whole bunch of statutes passed by Congress.
Geez, there was passage early in 1913 of the Webb-Kenyon Act, a long-sought federal statute against transporting liquor into states that wished to block its entry.