“I would invade all of northern Mexico along a 10 mile wide stretch”.
There are a bunch of sprawling cities in that first ten miles; Matamoros, Reynosa, Nuevo Laredo, Juarez, Nogales, Mexicali, Tijuana.
If you take them, you get millions of people, and a huge bill to modernize them.
I’l run my military potrol lines as far on the edge of those towns northern borders, but still within Mexico. Those towns themselves will make “keeping the illegals to Mexico” easier - sentry points just direct folks back into town.