Since the U.S. was going through it's westward expansion and Manifest Destiny phase, and since one of the goals of the early war of 1812 was to annex Canada, it seemed like this would of been in the interest of the U.S., especially since we did capture the capital of Mexico City.
At the time both the army command & the government were against acquiring so many millions more of (what they viewed as) non-Americans as well as the possibility of slavery spreading into Latin America.
This might have worsened our eventual civil war & in reality some rebels did try going to Mexico to continue fighting from there.
There was also agreement that Mexicans hated them for conquering them & it was bad enough taking Half their country; also - even then, what became the American West faced many generations of bandit raids into the U.S which hints that we probably made the right call leaving them be, even if they might have avoided a century of wars, dictators and bad governments.
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Summary - Too much trouble, already treating them shabbily enough as it was.