If we're bad at assimilation, then immigration is dangerous.
If we're good at assimilation, given modern communications technology, we should be able to assimilate people living in other countries. They can learn English and Western values online. They can access our books, TV, radio and online or mail-based educational courses from their own countries.
Therefore I propose the following immigration policy: only let in immigrants who already assimilated before immigrating.
There's no need to let in unassimilated immigrants and then try to assimilate them after they're here and hope it works.
Assimilation has a failure rate. If we assimilate them in their home countries, the failures can stay there instead of already being here. And even with a low success rate, we can still assimilate a larger number of people than we actually want to bring here (we can still pick and choose the best ones).
If you want to come here, prove it first by assimilating yourself remotely.
What if someone doesn't have access to the internet, or there is some other obstacle, so they don't have the opportunity to assimilate? Too bad. Life isn't fair. Our immigration policy should benefit our country by only taking people who found a way to already be a good fit before coming here (there are enough of them that people without internet access are not our problem).
Also, the best thing we can do to help underprivileged foreigners is to spread Western values to the whole world. We should be making it clear that Western values – the ones that originated with the Greeks, then the Romans, then the Western Europeans – are the only ones that bring peace and prosperity. Other countries can help their own underprivileged by adopting capitalism and limited government, by favoring economic and personal freedom, and by having a government which protects men from violence instead of violently oppressing its people.
There are a lot of people in the world. They can't all come here. Foreign countries need to improve. That's the only way to help everyone.
The U.S. needs to improve as well. It's in real danger from anti-Western ideas that have gained popularity internally. Bringing in more people who don't have Western values is making that problem worse. That problem is threatening to destroy the most civilized country, which is the best able to lead others to freedom and prosperity. It's in the interest of all men of good will, in all countries, that America remains a free and prosperous country that is capable of sharing good ideas with others.
America should be spreading its values to other countries, not bringing other values here. Sadly, a lot of the problem is that America is currently exporting anti-American values. The "intellectuals", media and "cultural elites" are predominantly anti-American. But thanks to the internet, anyone can help, regardless of where they live, by learning English and studying the ideas that made America great in the first place, and then communicating, explaining and teaching those ideas. The world needs fighters for ideas – the American ideas that came from Europe that came from Rome that came from Greece. Those ideas about reason and liberty are the only civilized ideas the world has ever known.
Also, immigrants are no threat to a free country. Immigrants with other values become a problem when the government meddles in men's lives, restricts liberty, fails to protect law and order, and redistributes wealth. Help fight the intellectual battle to save the U.S. from the authoritarian ideas of a giant, all-controlling government and we could then be in a position to reasonably (instead of suicidally) consider a more generous immigration policy.