The Bracero program ended in 1964 (started in 1942 because the US needed workers since men were being drafted for WW2).
The primary drivers behind ending the program were 1) union objections. 2) workers were illegally staying after their contracts ended.
That being said, if you could solve the problems with the system, a version could work. All of the in-processing was done in Mexico by US officials, but working in concert with Mexican officials.
Modern day problem would also be the Cartels. They don't want a safe, legal system because then BP can focus more on security and drug trafficking threats.