That's what will happen.
That won't happen. We can't even get Congress to pass the SAVE act, let alone define "subject to the Jurisdiction thereof".
Congress has neutered itself.
While it is true that the 14th Amendment empowers congress to resolve this, the text is as perfectly clear and understandable as anything. Section 5 is only like 15 words long.
Congress will refuse to act. That is what should happen; Congress should act. But that is not what will happen.