Interestingly though, there WERE concerns in President James K. Polk's administration about how Europeans and others might view the end result of the Mexican-American War in 1848. It's part of the reason the captured lands (California, Arizona, Nevada, etc.) were technically purchased from Mexico rather than simply snatched and annexed. I'm not sure why they feared the Europeans would be angry about it a ton, unless: 1. It would in their view upset the balance of power in the world or 2. It would make America look like a hypocrite for practicing methods similar to European empires against fellow "New World" countries. It unquestionably helped lower anger and tensions between the US and Mexico though after the war though (since the lands technically were not stolen).

The US government was of two minds about indigenous people. They'd establish treaties and then break them as the treaties became inconvenient.

Nobody could stand in the way of land speculators. This is what's behind Andrew Jackson's ( apocryphal ) "Mr Marshall has made his decision; let him enforce it" concerning Worchester v. Georgia.

The Mexican government could declare El Norte theirs but they really couldn't hold it. By the time railroads could be built it was too late for Mexico to pursue claims. Even then; fly over the border now. You see settlements that seem logistically untenable.

The incredible thing about the Texicans is that they simply refused to admit defeat against the Commanche. S. C. Gwynne's "Empire of the Summer Moon" outlines the persistent pattern of this phenomenon of memory loss in detail. There's some credibility to the theory of Walker Colt also having a hand in subjugating the Comanche. The Rangers really were hired killers first and foremost. This continued through the 20th century, with Frank Hamer leading the team that assassinated Bonnie and Clyde.