It depends, right? Prohibition of anti-bacterial usage in soap is unlikely to create black markets and mafias. Therefore prohibition is an effective solution.

Prohibition of alcohol does create black markets and mafias, so an alternate solution is needed.

Alcohol's effect is limited in scope. It affects the individual, affects the immediate surroundings, and perhaps their family. It cannot affect some one in another country.

The resistant bacteria can grow to a problem of global proportion.

Alcoholic drinks sold in a package come with warning labels. I've seen reports 1-2 drinks a day may improve longevity, but I doubt it would be acceptable to label every beer as "youth potion", you have to limit intake for possible benefit. For the soap, to receive a benefit also requires more than the label indicated.

The substance banned takes hours to kill the bacteria (according to the article), so I would say it's marketed in a mis-leading way. I doubt many people actually buy the soap thinking a multi-hour exposure is needed.