A ban on alcohol would result in benefit for public health and safety. Any tax revenue from the sales of alcohol is a secondary issue. The key issue is the prevention of alcoholism and drunk driving. Governments could always find other ways to raise revenue or other taxes to levy.
Cutting taxes is hardly a good idea. Taxes fund a lot of things the government does to improve the lives of its citizens. People are going to want to drink, and this will always be part of human psychology. It's been shown throughout history that alcohol bans never work or acheive their desired ends.