Can you bring us back to the place where I am meant to care about this? We are talking about people who have known no other country than their home country --- America.
And replace it with what, exactly? That clause [0] is, after all, what created uniform national citizenship, and eliminated varying and discriminatory state citizenship policies. Even if one agrees that the "anchor baby" problem is something that warrants limiting citizenship to combat (highly contentious proposition itself), simply blowing up the entire post-Civil War model of US citizenship is a rather brute approach with wide ranging consequences outside the immediate target area.
[0] "All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside."