They don’t have to change a word of it.
Section 5 gives them the power to define what “subject to the jurisdiction thereof” means.
They have already defined what it means with regard to certain foreign nationals and Indians.
I wish you were right. I wish congress could declare that an illegal alien’s sperm and womb are foreign territory, but we have to deal with the world as it is, not as we would like it to be. Furthermore, what do you think the chances are of Congress doing what you say they can do, and Obummer signing it? Almost as good as getting constitutional amendment.