The Gadsden Purchase, 1854
The northern Union Pacific Railroad route proposal had issues with snow in the winter, which still persist to this day, while a southern route would have to go into what is today, the southern parts of New Mexico and Arizona, but at the time it was the Mexican territory, known as the Second Federal Republic of Mexico, until its purchase by the USA. The Gadsden Purchase would resolve this issue, and such a route for the railroad was completed by Southern Pacific in the 1880's.
Correcting surveying error
The Gadsden Purchase corrected the American surveying error to make the southern border as initially intended. This correction cost the US Government dearly for their mistake. The financially-strapped government of Santa Anna, President of Mexico, agreed to sell the territory for $10 million (equivalent to $270 million in 2023).
Dragoon Pass railroad crossing
Dragoon RR crossing is the highest point in the entire Gadsden Purchase and is snow free, meaning it can operate 4 seasons without snow removal. Southern states, leading up to the Civil War, were concerned with being cut off from the California coast and Pacific Ocean. The Gadsden Purchase solved this problem.
US President Pierce was strongly influenced by Jefferson Davis, a strong southern advocate for the southern cause. While correcting the surveying mistakes made sense, the Gadsden Purchase also secured the souths access to the west. When the Civil War broke out, the Butterfield Overland Trail Stagecoach contract, which also operated through Dragoon Pass, was cancelled by the northern controlled US government and reissued with a northern route well out of the reach of southern concerns.
Some have said that Dragoon Pass was the reason for the Gadsden Purchase. While it was not the only reason for the Purchase, if Dragoon Pass had been impassable and if an alternative route could not have been found, then the Gadsden Purchase very well may not have happened.