In the history of man, has there been any Prohibition that has worked?
yes absolutely. Are prohibitions ever successful in removing ALL of whatever they are prohibiting? no.
We prohibit slavery, selling of organs, murder, and rape on a state and national level.
We prohibit nukes, biological, and chemical weapons on an international level.
The prohibition of unregistered machineguns is pretty effective actually. I disagree with it but I don't break it.
Many countries have successfully prohibited pornography, alcholol, exposed female body parts, etc.
In none of these cases are these prohibitions ultimately perfectly successful...but you don't see many women flashing a 'whale tail' in Saudi Arabia.
What do the successful prohibitions have in common? Serious enforcment who target ALL involved, and much greater agreement by the society as a whole that said item is 'bad'
For drugs, that means targeting the produces AND distributors AND users...as well as anyone who 'helps' them.
For illegal immigration this would mean targeting those who move illegal immigrants AND targeting illegal immigrants themselves AND targeting the businesses who hire them, be they big or small.