That is all false, the 1920s was a period of intense anti immigration awareness.
The laws they passed in the 1920s limited all immigration to 150,000 and most of those had to be from Britain and Northern Europe.
America of the period was (for practical purposes) all white, all English speaking, rural, and uninviting to illegal aliens. As late as the early 1970s the small numbers of illegal aliens lived in the shadows and tried to stay out of the sight of white America.
Those days are gone, now we are already a “multi-cultural, multi-lingual, multi-racial nation”, today Somali Muslims, Tibetan Buddhists, Mexican peasants, Asian tribal people, Middle Eastern Muslims from all the Arab nations flood here in vast numbers and never for a moment maintain anything other than open, mainstream, living.
As far as your theory that a Mexican peasant is better off in Mexico, at least 15% of them ( adult labor force) already have come to the United States. Ending the border controls and removing all complications and legalities would lead to the flood of hundreds of millions more newcomers from around the globe.
“The current migration of Mexicans and Central Americans to the United States is one of the largest diasporas in modern history, experts say.
Roughly 10 percent of Mexico’s population of about 107 million is now living in the United States, estimates show. About 15 percent of Mexico’s labor force is working in the United States. One in every 7 Mexican workers migrates to the United States.”
And we pay them to come...