I surmise: Because then they didnt have to suffer the indignities of detention and the inconveniences of being deported to a place they were unfamiliar with. (ie Veracruz, Monterrey).
The bottom line is that in the 1950s, deportation was tried and deportation worked, and 10 years later, illegal immigration was at low levels. ONly after the 1965 immigration law did illegal immigration ramp up again.
We will need to repeal the 1965 immigration law if we want to fix illegal immigration.