There's a sort of disturbing inference that whiteness=stability.
The history of Argentina should probably disprove such assumptions. In any case, Brasil was able to implement Branqueamento well for two reasons:
A) They had some land in the southern cone more suitable for European agricultural immigration. This is why southern Brasil, Argentina and Uruguay received so many Italian and German immigrants--because the Southern Cone was temperate enough for the European crop package (and because it had land for ranching).
B) Brasil in particular had access to Portuguese immigrants. Portugal, being poor as hell and with no attractive targets of its own (Angola and Mozambique were terrible for settlement), sent hundreds of thousands of Portuguese abroad, mainly to Brasil, even after Brasil declared independence.
Mexico has a few factors going against it. One, of course, is the US; most white settlers into Mexico were, esp. in the north, English or American. This would draw the immediate interest of America, and would probably lead to to more "Texas" style intrigues.
Secondly, the rest of Mexico has a much hotter and less temperate climate. Furthermore, Mexico is very far from Europe in terms of ocean distance, and has to compete with both America and the Southern Cone for European immigration. And then you consider the mountainous terrain and, furthermore, the entrenched criollo elite owning a lot of the land. I don't really see a Mexican Branqueamento as a probable option. They received Euro-immigration in OTL, but it was never going to be an Argentina or Southern Brasil in terms of population demographics.
Good question, there's alot to this.
First, Mexico had a large native population, which I don't think Argentina or Brazil had at the time. Alot of
unoccupied land helped lure Europeans to Brazil and Argentina.
I'm not sure if Mexico's land was worse for farming or ranching than parts of South America, just occupied.
I imagine there are alot of other reasons.
1. Occupied land by large native population.
2. The fact that there is a large population would make it difficult for Europeans to "dominate" the culture in the manner that they could elsewhere and preferred to go someplace familiar than try to melt into the native Mexican culture.
3. Since there was a native population already, there was less interest in altering that balance of power by "recruiting" immigrants whom might provie political and social rivals.
4. Mexico was less appealing due to instability of constant wars from 1820 to 1900 (Independence, European invasions and many, many coup-d'etats).
Note that, around 1900, Argentina's per capita wealth rivaled the United States. It was only in later years, for a variety of reasons, that Argentina fell so far off the pace. Corruption is always a big issue.
Mexico wasn't poorer due to racial reasons, mainly cultural. Dominated by a diverse group of local tribes, there was a less unifying source of language, purpose, culture, economy etc that held back Mexico. As always, corruption.
Argentina was largely mono-cultural (Spanish and Italian dominated/es).
A good comparison for Mexico would be India - large, non-unified population
A good comparison for Argentina would be Korea - more of a monolythic population.