The Germans courted Mexico as an ally in both World Wars, in an attempt to busy the US with a war at home. The Prize? The American Southwest. Had the founders been more concerned with sunny beaches and oil, Manifest Destiny would have extended our southern border to Panama.
President James K Polk a principle implementer of Manifest Destiny, sent General Winfield Scott and his aide Capitan Robert E Lee to conquer Mexico. They entered the Halls of Montezuma, defeated and threw out Santa Anna for good. They conquered Mexico.
Polk left Mexico alone. He did not want it.
Mistake? perhaps, but it was also a terrible burden better left alone.