To be honest, though, that charge has been leveled at every immigrant group that's come before. It generally takes 1-2 generations to "fully" assimilate. They said the same thing about the Irish and Italians in the old days.
Heck, you go back three generations and you have my great-grandparents, who all came over from Poland / Eastern Europe and settled on the south side of Chicago--with all the other Poles. Three generations later, when I think of my "cultural heritage" I consider it far more dominated by American history prior to my great-grandparents' arrival, which is frankly British--even though I very well may have more Neanderthal DNA than English in my heritage (according to 23andme).
The charge of "lack of assimilation" is commonly leveled at any new groups of immigrants. And then a generation or two later, when they've assimilated, we forget that and apply it to the new group.
I also think that SW USA culture in particular might be as much of a "meld" as an "assimilation". Most of the SW USA was at one point much more Mexican than it was American--or more accurate is to say it WAS Mexico before the Mexican-American war. You can't erase that cultural impact out here. Heck, every 4th grader has to do a project on a Spanish Mission in California. Around here, Mexican food isn't "Mexican food", it's just food ;-)
I completely agree that there have been times when immigrants met a lot of resistance, even hostility. (It's true of every country, BTW. In nearly every case, much worse than here. For example, could an American emigrate to China and ever be considered Chinese?) The resisters were and still are called "nativists." And it is also true that as immigration sources moved eastward and southward in Europe, the resistance was greater. More linguistic, religious, and other cultural differences. But they did assimilate,and within a couple of generations, they could consider themselves "old-stock" Americans and even be among those resisting new waves of immigrants.
I'm not a nativist. I know that we've been enriched by immigration, both financially and culturally. I'm glad that we are a nation of immigrants. But I do want immigrants who become citizens to give their allegiance wholeheartedly to the United States of America. If they can't do that, then they should just remain legal residents. And the larger the wave of immigrants, the more unlikely it is that the immigrants rapidly assimilate.
You raise another good point about why Mexican immigration has not followed the usual pattern. You know, in New Mexico anyway, the old Mexican-Americans, those whose ancestors lived in what is now the United States when it still belonged to Mexico, are sometimes as impatient with the recent Mexican immigrants as Anglos are.
Here's a video clip on immigration from Ronald Reagan:
https://www.facebook.com/NowThisNews/videos/308836506423173/.
