You kinda contradicted yourself there.
Yeah I know, what I meant to say was that as long as they fight less it is ok to have elites. Many seem to simply blame them and think that without them everything is solved. Which I find incredibly naive. In the case of the US, it was an elite riddle nation. This did cause a Civil War but in the end with the appropriate measures their meddling was somewhat solved (they still meddle but less).
Another thing would be to keep the USA much weaker. Having the south win the ACW isn't enough because it is too late a POD. Instead, the Mexicans could be more Indian-friendly and help the likes of Tecumseh, Blue Jacket, and the Red Sticks. The Indian Wars only helped to increase US militarism which for all intents and purposes destroyed Mexico as a major power in the area. Even after the Mexican-American War the US, or at least enterprising American citizens, kept interfering in Mexican affairs. Hell, a ton of Marines even went to help the Yucatan against the Mayan rebels, though they ended up getting embarrassed and taking a ton of casualties.
I know the Civil War is a bit too late (unless you make it happen sooner). That is why I proposed turning the Oregon conflict with Britain into an Oregon War. This would happen sometime in the early 1840s. It is better if Britain wins closing the US off the Pacific. But even if the US wins and gains what is for us British Columbia it still lost a major trading partner. And if Mexico plays its cards right it gains a very strong ally, a trading partner needed for an export based economy (always a good thing), and an investor.
I also suspect Cuba would be annexed to Mexico sometime around here as well (with the help of its new ally).
Another option are the numerous Indian Wars that Mexico could unofficially sponsor during the removal (if it happens as in OTL). Although the removal ended by 1837/38, the Oklahoma equivalent could be a very strong ally of Mexico as well. It might even be set as a "buffer state" between both nations.
Then there is the Civil War. If the south wins, good. If the south balkanizes into several "cotton republics", better. If the south balkanizes into several "cotton republics" filled with inner strife that put stress in the US, much much better.
There is also a large black underclass (or slave class). The staunchly abolitionist Mexico could use both to stir rebellion in the US and as immigrants into Mexico.
Yes the Indian Wars helped increased US militarism. These other proposed wars could do the same (or the opposite as the US was also known for heavy isolationism and xenophobia in its early years). But Mexico will also be having similar wars that will help foster a Mexican militarism.
The Castas War might still happen (and it might include parts of Central America).
We also have a war against Spain to annex Cuba (maybe a second one much later to free the Philippines).
There will be, and must be, a Reform War at some point as well.
Finally it is my guess that Mexico will also suffer some Indian wars at some point. The Navajo in Alta-California / Arizona wont be to happy once Mexicans and Immigrants start moving there.
And I also considered the possibility of a Mormon War. Even after a Reform War, as in OTL that proclaims "freedom" of religion. I am very sure Mexicans will not be very nice to the Mormons in the north. Not just because of the religion issues but they might still see them as unwanted Americans. Honestly, I can see a Mormon genocide happening at some point. Even Mexico which professed equality and liberty for all since is independence (it failed in the equality part in OTL) would be capable of committing some sin. Plus we are talking of making it the major world power this does not necessarily mean a good one.
So yeah by the early 1900s both the US and Mexico are militarized and ready to face each other in a Great North American War.