If so, then the Constitution is a suicide pact, because people by the hundreds of millions can just show up and they are citizens.
There is a logical problem with this analysis. Say a woman is a citizen of China. She visited the US briefly to have an anchor baby. Then she went back to China with the baby. The baby grew up in China and eventually died there. Now what jurisdiction is the person born subject to? Breifly he was subject to US jurisdiction. But that is true of anybody just visiting the US at one time or another. What is so special about the time of birth in describing what jurisdiction a person is subject to. I visited other nations, but dont consider myself a person subject to their jurisdiction, that would be an absurd discription. Im subject to US jurisdiction pretty much all the time. The 14th amemdmemt does not specify that people born under US jurisdiction are citizens. It says that people that are both born here, and that are under US jurisdiction are. People who just visit, even if they just visit when they are born are not genrally subject to US jurisdiction.
No, their children are, if born here.