John Derbyshire tries to explain why we want unrestricted immigration in his "The Great Syllogism". I think he's mixing together pragmatic and principled arguments.
We should allow unrestricted immigration not because it will result in a more racially-balanced society, but instead because it's the right thing to do. Unrestricted immigration is right because free trade is right. No one should have the right to restrict my trading, or my movement.
If anyone tells you that there should be any restrictions on immigration, ask them why their argument doesn't apply to, say, New Jersey. If we should have the right to keep people from Russia out, why shouldn't we have the right to keep New Jerseyans out? Our country has been very successful by allowing unrestricted immigration between states.
Now to be specific about John's arguments. In his point #2, he says that we have developed an equally strong desire for racial equality. Perhaps we have, and perhaps any kind of successful action will have to take that into account. We should also be clear that the first and second part of #2 contradict each other. Maybe he's right, but if he is, then we have to give up one or the other parts of #2. He makes this point in #7.
John says in #3, "Our very best efforts at creating a meritocratic education". Get real, John. The vast number of K-12 students in America spend their day in the gulag. Stuck there, doing pointless activities, told what to wear, where to go, when to go, and expected to learn? This is not "our very best effort". Our school system is the very model of modern socialism. It is pitiful, and produces pitiful results, as John notices.
John gets to the meat of the problem with immigration: "10) Therefore the manual class is seriously under-staffed." Ironically, the people most likely to be against unrestricted immigration are those who have most recently come here. Expanding the labor pool will reduce the need to pay them more.