Alcohol is too easy to produce and banning it would only help organised crime. Remember the prohibition era of the 1920's/30's?
Sometimes I think it would be awesome if you could, but people could literally make alcohol from the weeds growing on their lawns. There's tons of how-to books available, and the internet is replete with DIY information to make booze. How are you going to enforce a ban on something like that?
There are problems with alcohol being legal. Working as a bartender has shown me how many people are drunk drivers, and how many people get violent as a result of alcohol. Alcohol is fun if used responsibly, but people need to remember that it is a drug. While banning it may remedy many problems, such as drunk drivers, certain related diseases, and perhaps domestic violence, it will cause more damage in the long run (and we have history to show for it.)
Banning the sale of alcohol just won't work.