The original intent of "subject to the jurisdiction of" means areas of the US not under foreign military occupation, or diplomats, and anyone working with diplomats in a diplomatic mission. And probably includes the inside of the embassy/consolate. And maybe the UN building. But it was not supposed to mean anything to do with nationality. And I think "being here illegally" is also very problematic. Like are the enslaved people here "legally"? The 14th amendment was used to give citizenship to enslaved people. Enslaved people aren't considered people in terms of citizenship, and the moment slavery was outlawed, do enslaved people become "illegal immigrants". So are we just gonna remove citizenship from every decendent of an enslaved person in the us?

How do we even know who is here legally and who's not. And what if we found an "illegal" immigrant that entered in the 1900s, are we gonna deport every of their decendents?