You make some excellent points, and describe the issues splendidly. However, at it's root is the word and concept "illegal".

I don't doubt that folks are economic refugees. That's fine. It's not an excuse for breaking US laws. So robbing banks is illegal. Well, what if the bank robber is an "economic refugee"? Is it now permissible? Why not? How about mugging people, as long as they are Caucasian, and not "economic refugees"? After all, a case can be made for needing to distributing the wealth, and an economic refugee clearly needs the money.

Mexico will not tolerate Americans overstaying their visas. How do they justify - Oh, I forgot. "Economic refugees".

Deport 'em, all of 'em, and close the border. Then they won't be economic refugees.

Done.