Interesting question. I'd suggest that the answer is yes, but it would take time - given that the best people would move to places that offered the greatest economic opportunity, creating a positive reinforcement loop for places that offer better economic policies. To a certain extent this is already happening given the effects of pro market policies.
The problem is that you'd first have to reduce or eliminate some of the entitlements that have been strangling developed countries that were created at a time when their cost wasn't nearly as much as it is today. Eligibility for benefits would need to be reexamined to make an open immigration policy more feasible. The article in the Atlantic also brings up another issue - "if you're coming from a place that has a problem, you are probably part of the problem, and if you move to a new place you might bring the problem with you."
This isn't academic given how there has been significant migration from "blue" states to "red" states which are seen as more business friendly in the US. Glenn Reynolds at Instapundit argues that "someone needs to set up a “welcome wagon” to explain to new immigrants why the states they’re moving to shouldn’t become more like the states they left". Further, Mickey Kaus notes that overly generous welfare systems can reduce the need for social integration breeding resentment and may even be a cause for terrorism (Slate via Instapundit).
More here (TheAtlantic via HN):
If wealthy nations open their borders, won't native workers lose their jobs or see their pay shrink? Not so, according to Clemens. He and his co-authors, through study of all the available economic literature, have found that decades of immigration of tens of millions of people to the United States has reduced real wages for the average American worker by fractions of a percent, if at all. Meanwhile, immigrants to the U.S. from developing countries can increase their income by 100 percent, or 1,000 percent. "Immigration is very, very far from being a zero-sum game of 'their poverty or ours,'" Clemens wrote in 2010. "Within ranges that even slightly resemble current migration levels, it is rather simply 'their poverty or their prosperity,' while we remain prosperous."
Clemens's research also challenges the notion that immigrants take away jobs from Americans. In agriculture, for example, he has estimated that for every three seasonal workers who are brought in, one American job is created across all sectors. Directly, workers need managers, and more often than not those managers are Americans. Indirectly, workers buy things, which means more Americans are needed to sell and produce those things. And yet, Clemens told me, "when a bus of 60 Mexicans is coming up from the border, nobody looks at it and says 'Ah, there's 20 American jobs.'"
But some immigration restrictionists have far bigger worries than workers losing small percentages of their salaries. There are many possible negative consequences of open borders. Naik points out that "political externalities" may be a major drawback of allowing anyone who wants to move to stable, wealthy nations to do so. Gallup polls have found that 700 million people would like to permanently move to another country, many of them from developing nations with failed political systems. If the U.S. or another wealthy nation were to see a sudden large increase in immigrants from these countries, it's possible that the new populace will vote for bad policies in their new home. As Naik puts it, some people believe that "if you're coming from a place that has a problem, you are probably part of the problem, and if you move to a new place you might bring the problem with you."