One thing we've avoided doing during the immigration debates over the past few years is consider the whole of our immigration policy, including legal immigration, which is a consuing web of quotas and restrictions. I think Jeff Jacoby is on to something here when he suggests that it's time we consider scrapping the whole thing:
Yet for most of US history, the government’s approach was radically different. Immigration was largely unrestricted. Most peaceful foreigners were free to move to the United States. Certain categories of individuals might be excluded by law, but only because they were deemed genuinely undesirable — for instance, those suffering from a “ loathsome or a dangerous contagious disease.” Apart from the disgraceful and racist Chinese Exclusion Act of 1882, it wasn’t until the 1920s that Congress began imposing broad arbitrary limits on the number of people who could come to America, or the countries they could come from. Driven by a nativist backlash to what had been the greatest wave of immigration in American history, Congress for the first time created the quotas that are now so entrenched in US immigration policy.
Economically, such quotas are indefensible. Lowering immigration barriers is one of the most pro-growth measures any country can adopt. But our current quota-based system is politically harmful as well. Thanks to its capricious restrictions, immigrants are deemed “illegal” not because they are objectively unsuited to be Americans, but because they don’t fit within a random numerical cap. What’s worse, those very restrictions create the distortions that induce so many industrious immigrants to cross the border unlawfully. That in turn generates the anger and suspicion that have made our immigration debates so rancorous.
I don't know that we can or should go back to a "largely unrestricted" policy. There was a time when it made sense for us to have basically open borders, when we were a young nation and needed warm bodies to fill all that space. Our needs are different now -- we can be a little more selective by defining what kind of immigrants we want, and there are too many people around the world who wish us harm and don't need the help a free pass would give them.
But we should be a lot less restrictive, and we should worry more about the type of people we encourage than their country of origin and perhaps even their skill sets. We should want people who want to become Americans and live by the Western values that have sustained us. Having a system so capriciously byzantine that it encourages illegal entry does not foster that kind of melting-pot effort.