Well, unless one also controls demand, along with supply.
Never has been a case of a fence stopping smuggling, that I know of.
There meeds to be a multi-prong attack. Jail time and MASSIVE fines for employers of illegals, a 2 zone fence with a land mined defensive zone between (It's a DEFENSIVE measure!), and sponsoring for any new immigrants, with the sponsor fully responsible for any crimes committed by the sponsoree.