If you stop people... You also tend to stop the trafficking of other illegal items/substances.
In order to "stop people", you would need to close the borders which would be disastrous policy. Even the Republicans wouldn't be so stupid. As previously stated, the majority of contraband enters the country not by people sneaking across the border, but by people entering legally at ports of entry. A fence isn't going to help you with that. What would help, is improving the technology available at ports of entry to be better able to detect hidden contraband.
As for your comment about how every nation needs secure borders for the safety of the citizens, immigrants, both documented and undocumented, commit less violent crime that natural born citizens. If we want to act in the interest of safety, it would perhaps be best to deport the Americans and let the immigrants have the country. While there is certainly some criminality which crosses the border (as mentioned above), a fence is a pretty piss poor way of combatting it (as mentioned above).