Where do you draw the line? It looks like it should allow denial of U.S. citizenship to the children of illegal aliens or Asian tourists, but what about legal immigrants who are intending to become citizens but haven't been in the U.S. long enough to complete the process?
During the heyday of European immigration to the U.S. in the decades before 1921, there were a lot of children born to immigrants who grew up as Americans. Many of them gave their lives for the United States in WWI or WWII, or served honorably before producing hordes of monolingual third-generation Americans. Is the citizenship status of people born in the U.S. to legal immigrants to be questioned?
Not at all. It's very simple. According to the Constitution they are not citizens. When their parents are naturalized so are their minor children. If the children reach the age of majority before that time and qualify for naturalization by fighting for America or other appropriate means, I see no reason why Congress would not pass laws defining and securing such means. That is how it was intended and should be.
Legal immigrants in the process of acquiring citizenship clearly fall under the "subject to the jurisdiction thereof" clause (they are in the country under proper legal authorization and are answerable to American law). Thus, children born to such persons on US soil are immediately US citizens.
Of course, the problem isn't with legal immigrants.