You mention Europe as our historical sources of quality immigrants, correct me if I'm wrong, but aren't Mexican's mostly of Spanish descent, just like Americans are mostly of English/Irish/German/Italian descent? And the last time I checked Spain is in Europe.
I don't have any magic means for getting 2nd and 3rd generation immigrants out of poverty, but I do know that America has a unique underclass problem in the industrialized world.
And I don't think immigration has much to do with it, there are not a lot of immigrants in Appalachia.
Compare the social services in the US vs the rest of the industrialized world. Outside the US, you tend to see things like cradle to grave, and those are not magic. They are expensive, but they are not magic.
A valid debate would be the cost vs benefits of European or Canadian style social services vs what the US has.
Lastly, I don't think low reproductive levels are responsible for the lack of European immigrants.
Ireland still have quite the high birth rate, and they aren't falling over to come the the US, like they did during the famine. Their present standard of living might have something to do with that.
You don't attract masses of immigrants from places that have a standard of living just as high as yours.
And I'm not sure what you mean by East Asians having a higher but less creative IQ?
I suspect your prejudices are formed by the fact that East Asians can't walk into the states, and that means they are less likely to be common laborers and more likely to have a formal schooling background.
If the US bordered India, and Mexico was across the ocean, things would be reversed.