There was an interesting article posted awhile back, it pointed out that the children of diplomats born here are not US citizens.
The legal fiction is that diplomat remains domiciled in his home country, even if he stays in this country for years at a go.
Children of transient visitors (non resident visa, and via waiver situations; not just illegals) should likewise obtain the citizenship of their parents' domicile. This is what "subject to the jurisdiction" meant when it was passed. As interpreted (incorrectly), the words are surplussage. Meaning that even if "subject to the jurisdiction" was removed from the 14th amendment, children of diplomats would still be citizens of the their home country - ergo, those words aren't in the 14th amendment to protect the citizenship of the diplomat's kids.
Unless the Diplomats can show that they were here illegally.