Countries subsidize rural living because it enforces their control over the frontier.
The United States is difficult to invade because of the oceans surrounding it and the many people with guns in the interior that'll take shots at armies.
If you put everyone in a few cities on the coast, the USA becomes easier to invade.
I can't find any source suggesting this was actually a thing in the 30s and 40s. All I can find is the Zimmerman telegram from a hundred years ago which the Mexicans weren't exactly enthusiastic about.
In any case, I doubt there is any realistic threat of a Mexican invasion beyond fantasizing from political fringes.
Quite the contrary: an empty countryside would make invasions harder because there would be no infrastructure: no roads, no bridges, no tunnels, no electricity, no water supply, no opportunities for shelter. Everything would have to be shipped from outside or built by combat engineers, putting an immense strain on logistics and slowing operations to a crawl.
