Today the outflow is minimal, immigrants know the good life when they see it. And they also know the government has no intention of making them go back if they are in the US illegally. On the contrary, they send for their families to come over. The whole system has turned into a scam.
I guess it is in a way because we tend to think people who came always stayed but then again it is hard to go to another country and culture, learn a new language. Without the safety nets we have now though many Europeans and others went back ---which back then meant another long boat ride ---not easy. Without welfare, many of today's immigrants would also go back, we see many now who won't learn the language of this country but now they don't have to because they can just depend on taxpayers to provide for them if they don't care to make the effort.