Your description of the history of the Mexican War is at best one-sided, completely ignoring those aspects that reflect less well on America.
A great many prominent Americans at the time believed the US to be in the wrong on the war, including Lincoln, US Grant and many other military officers, Thoreau, ex-president John Quincy Adams and essentially all abolitionists.
Nevertheless, Mexico controlled the area (very loosely) for less than 25 years. The US has controlled it for closing on 200 years at this point. It is ludicrous to claim that legitimate title has not transferred.
It’s a good thing that Mexican troops started the war, then, isn’t it? They over-ran a small US outpost and then started to move towards a larger one near the coast. This was after a new Mexican government repudiated the terms of a treaty they had agreed to earlier under a different dictator, and they had refused further negotiations with the US over the Tex-Mex border sticking point. Whether or not that was worth the full-scale war that soon came might be debated, but at the time, it was a good enough reason for Congress to declare war.
After Texas Independence, the war with Mexico was almost a foegone conclusion if Mexico in any way physically objected to Texas statehood, trying to claim the disputed border, or in any other way.
Sorry, it may not seem fair to some today, but to those along that border at the time, who were contending with Mexican incursions, Apache and Commanche, it was very serious.
That two year war, though the relative strengths of the two nations was one sided, was not so one sided in and of irself. The US forces invading Mexico were much smaller than the Mexican Armies they faced, and they were about equally armed. In most cases you had smaller US forces attacking well defended, fortifications manned by larger numbers. What that smaller force accomplished is fairly amazing on its face.
The bottom line? The Mexicans lost. US troops occupied their capitol in Mexico City and the Mexican government ultimately signed the treaty of Guadalupe Hidalgo. That's the bottom line. it was signed in 1848 and allowed the US to take possession of the current US southwest, which the US paid the Mexican government millions of dollars for, and which also guarunteed Mexican citizens who were cauight up in the exchane their property rights in the new territories if they elected to stay. Most did.
The land was very loosley controlled by the Mexican government at the time (with the exception of Santa Fe perhaps and the lower California coast) and mostly empty.
A comparison of the relative prosperity, freedom, and rights, and peace of the two seperate areas today (those lands ceded and the rest of Mexico) tells us which region benefited most.
What the re-Conquista movement is proposing would not only be terrible for the citizens in the areas...it would quite simply lead to a bloody, ut fairly short war...with the same outcome as 1848. property ownership.