Mexico does this and I suspect the US allows it for this reason.
Mexico uses illegal immigration as a pressure release valve to bleed off poor male workers from their society. Without it there would be a revolution in mexico, and a revolution on our border. That is why I suspect the US allows this to go on.
Bingo! Cheap labor and a stable political state next door. A win-win for the tax and spend political culture in the US.
Sounds familiar doesn't it. The US has been practicing this policy in Central America since WWII. What is new is offering refuge for the third world's political rabble in such massive numbers.
We used to just give them guns. Now we give them a home and unfettered access to our publicly financed, social, safety net. A win-win for the new generation of economic despots we prop up.