Impossible Immigration Swap

Will Wilkinson offers the provocative suggestion that ending birthright citizenship might be beneficial from a cosmopolitan point of view since it might make people more open to higher levels of labor market integration. His model is the European Union:

When Britain opened its labor markets to Polish workers in 2004, the gap in average income between the two countries was about as big as that between the United States and Mexico. But per capita GDP in Poland has improved markedly since then, hastening the day when Poland provides a robust market for British goods – and possibly British labor, too. Similarly, by 2012, Romanians and Bulgarians, who are on average poorer than Mexicans, will be able to live and work in rich countries such as France, Germany, and Britain. It’s worth noting, however, that not a single EU country has a birthright citizenship rule like that in the U.S.

I suppose I don’t really see the causal link here. What is it about saying that US-born children of Mexican migrants won’t be American citizens that would make people open to much higher levels of legal Mexican immigration? Normally when I see people objecting to birthright citizenship, what they’re objecting to is specifically the idea that it creates undue obstacles to deporting undocumented migrants or else that it creates an undue incentive for Mexicans to migrate. In other words, people upset by birthright citizenship are generally aiming at it as part of an overall program of reducing the number of Mexican-born people living in the United States. So I don’t see what the Wilkinson proposal is going to accomplish.