Not much incentive to do that when they can send their unwanted people north and they will earn more signing up for welfare than they could possibly earn working back home.
Particularly when they can earn even more working for cash on the side or under an assumed name.
That's what's wrong with "Build the wall". Walls are nice tools, but they must be defended. Part of the defense is reducing the incentive to cross them.
We need to cut illegal aliens off from welfare, work, licenses, schools, everything.