This is what has been puzzling to me--what the long game is on this EO when The constitutional amendment seems so clear on its face. The whole thing stands or falls on the meaning of "jurisdiction" as you rightly point out. I liked R R Reno's perspective in a recent article referencing the concept of adverse possession in the common law, specifically to address situations where someone squats on property for a certain length of time uncontested. For those who have been living and working here for many years and working with tacit permission, and under a legal framework that tacitly permits it, or even invites it, a path to legal status seems reasonable. They have entered our jurisdiction, tacitly, so to speak. But for the recent arrivals, and the birth tourism abuse, that is another question.