They don't return home because they can't reasonably come back. If you have to pay a fortune to a mule to smuggle you in or take your chances crossing on your own, you aren't going to make that back and forth journey.
The visa requirement for Mexicans is what led to the current situation.
Agreed, but that is where politicians should have been focused, and they weren't.
They had their chance back in 1986 when they passed the first amnesty bill but didn't follow through on the borders.
They could have done it right but didn't do anything.