I strongly believe the American choice was a strategic decision made by a group of highly intelligent individuals.
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Texas, California, Florida, totally unimportant backwater states, right? No Latin American culture, ethnicity, political or religious influence to speak of.
Whether Texas or California, the land that is now the American southwest was almost completely empty before the Mexican War; about 80,000 hispanos, or about 1% of Mexico's prewar population, mostly in New Mexico and southern Colorado. They were very, very isolated, living in "islands", and were already dependent on the US, not Mexico, for trade <http://web.archive.org/web/20070517113110/http://www.pbs.org...>. The American takeover and attendant influx of settlers completely changed the region; by 1860 California alone had 380,000 people] <https://en.wikipedia.org/wiki/Demographics_of_California#Pop...> and was a US state.
*85% of Mexican Americans today are from post-World War II immigration.* As late as 1970 <http://www.pewhispanic.org/2013/05/01/a-demographic-portrait...> there were five million people of Mexican ethnicity in the US, including one million born in Mexico. Now there are 33.7 million and 11.4 million, respectively. The number of people of Mexican ethnicity has grown by ~16X in 75 years (from ~2 million in 1940), while the US population has grown by ~2.5X. Had the Mexican-ethnic population grown by the same rate as the broader US there would be 5 million today, not 33.7.
History, even recent history, has been rewritten in peoples' minds by popular culture. Los Angeles's stupendous growth in the first half of the 20th century was driven almost entirely off of internal US migration. So many Iowans moved to LA that it was joked that southern California should be renamed "Caliowa". Almost everything we think of about the city, demographically speaking, is a post-1970 phenomenon.
According to Census estimates <http://web.archive.org/web/20080912052919/https://www.census...>, the city of Los Angeles was 7.1% Hispanic (almost all Mexican, of course) in 1940, and 15-17% in 1970. In 1990—let me repeat, two decades later—it was 39.9%. The non-Hispanic white population went from 86.3% in 1940, to 61-63% in 1970, to 37.3% in 1990. As of 2020 <https://en.wikipedia.org/wiki/Los_Angeles#Race_and_ethnicity> the city is 46.9% Hispanic and 28.9% non-Hispanic white.
"We didn't cross the border; the border crossed us" is only true for the aforementioned hispanos. If alien space bats had rotated the contiguous US 180 degrees in 1945, all other Mexican Americans would be living in Buffalo and Portland and Boston and Rochester and Detroit. Those cities would be known as the home of Cal-Mex and Tex-Mex cuisine, not LA and El Paso and Phoenix.