Exactly "subject to the Jurisdiction thereof" has been contorted to mean that just because some tourist (or, in this case, someone who sneaks into the USA SPECIFICALLY to drop a baby to gain U.S. Citizen BENEFITS), is NOT subject to the "Jurisdiction", which was meant for INHABITANTS of the USA, NOT FOREIGNERS.
To think a vacationer can drop a baby in the Country, just to gain Citizenship automatically, doesn't even pass the smell test.
Fortunately for them, Congress and the Courts have an endless supply of this