To your first point, you can buy the land, so Mexico is compensated.
However, the problem with trying to force people back is, what are you forcing them back to?
If I were an illegal alien, and my choice was a very difficult life or to jump off a cliff to certain death, do you really think that by making my life difficult or impossible that I’m going to jump off that cliff?
See if they use it.
I doubt they will.
As bad as Americans think Mexico is it is one of the world's better countries to live in. It can feed its people for one thing, and that's always important. Plus with the United States right next door they have relatively unlimited access to the most advanced science and medicine possible anywhere.
With their Subtropical Climate they don't need to expend much effort to keep warm either.
For the qualified higher education is essentially FREE ~ their university system is based on the European system.
Unemployment in Mexico is 4.5%