Your idea won't work. It makes too much sense. So those in power will automatically reject it. It is a good idea, though, and I would love to see it done. When I was under forty I thought of the same thing. Ship them back posthaste and bill the Mexican government for the costs of catching them and returning them. We could take it out of the foreign aid each year.
"Ship them back posthaste and bill the Mexican government for the costs of catching them and returning them. We could take it out of the foreign aid each year."
Now there's an idea! And ship them to the southernmost point of Mexico, AFTER getting DNA, mug shots, and fingerprints-- which we normally don't do right now.