So I went into a wikipedia death-spiral, and ended up reading Mexico’s thoughts and response to the Zimmerman Telegram.
Basically, Mexico wasn’t stupid. They easily figured out many reasons it would be stupid to go to war with the U.S. and attempt to take Arizona, New Mexico and Texas. These were practical reasons they didn’t entertain the idea, not philosophical reasons. They would have gladly taken back all their ancient territory if the Kaiser could wave a magic wand and make it happen.
Anyhow, in the long-term, they knew the U.S. Military would eventually respond, and surely crush them. In the short-term, they considered it impossible to handle a hostile and well-armed civilian populace in the territories they would wish to take.
Just sayin’ Stupid, I know, since the 20th century is, like, ancient history, right?