[GrandEagle]

Again, if one is physically present in a country, you are "subject to the jurisdiction of" unless you have diplomatic immunity. If not, then we would be helpless to do anything with them no matter what they did. If they are not "subject to the jurisdiction of" then we cant arrest them, detain them, or do anything with them - they are not subject to the jurisdiction of out nation.
Again, this clause is included so that US possessions are included in the clause, not just States.

[thoughtomator]

But if they are subject to the jurisdiction of the US, then they wouldn't be here in the first place. So the actions of the illegals themselves deny the basis on which citizenship is granted to the anchor children.