One small point: it’s not a “reacquisition”, it’s an out and out conquest. The Spanish and then Mexican presence and influence was always minimal in the SW. They never had the settlers or armies to really “own” the area, and their influence consisted mostly of a few small, isolated forts and missions. It belonged to the Comanche and Apache until Texas and American troops resolved that issue.
California - that’s a different story.
Suzy, don't you believe it. The Mexican population of California in the 1840's was in the 5,000 range. There was a somewhat larger mestizo population centered about the missions, the offspring of the few soldiers and the mission Indians.
More Mexicans entered California illegally last year than ever entered in all the years as a Mexican (or Spanish) possession. The best picture of pre-gold-rush California, IMHO? It's in Dana's classic, "Two Years Before the Mast."
There were so few settlers in California, that at one time The Czar was considering grabbing it for Russia.