Emigrants to a country do not give the country they're leaving a claim to the area.
Otherwise, the US would be split among the European nations.
And Mexico of the 1840s didn't have a collective identity. The missions in the north just want to continue life as is, and the few non-religious Mexican settlers mostly wanted to get away from the Mexican central government.
The main other settlers were Anglo-Texans or European immigrants who did not really feel ties with Mexico. The former of those two groups vastly outnumbering every other mentioned group.
I don't know about anyone else, but I've never argued that Mexico being a first world country on part with the US is easy or likely - just that adding Mexican territory to the US is not necessarily going to be better for anyone.
And again, "being part of a wealthy country" is not enough to produce regional prosperity.
Why is it going to develop more?
Why did Arizona, New Mexico, and Nevada develop? Because they were in a wealthy country and in between the two most habitable ends of it.
Baja California and far northwestern Sonora would most definitely be more developed as part of the US. The region is right next to California, holds potential spots for the US's southernmost and southwesternmost ports, and has a pretty habitable region encompassing San Diego, Mexicali, and the surrounding area. It also has the mouth of the Colorado.
Instead of needing to build the railroad all the way to California, they could build it to a port in the Sea of Cortez and go around Baja. Or they could build a railroad down Baja, with a port at the southernmost tip, from which circum-American trade could take place. After the construction of the Panama Canal, it will become even more useful.