I must disagree. If Congress were to take the position in a statute passed under Section 5 of the Fourteenth Amendment that "subject to the jurisdiction thereof" does not include children born to aliens not legally resident here, then the question would be addressed by the Supreme Court. It would of course depend on the ideological make-up of the Court at the time the case comes to them, but in fact the Court has never directly ruled on the matter and the view of Congress expressed in the "enforcement" legislation would count for something, though not dispositive.
And I think "subject to the jurisdiction" ought to be fairly interpreted to exclude someone born within the United States to foreign nationals who are not lawfully resident in the U.S..
If a foreign military force were to invade U.S. territory, would children born in the U.S. in the course of that military campaign to parents part of that military force be considered U.S. citizens? I think clearly not, and one should apply similar reasoning to foreign nationals who invade not by military force but rather by stealth or subterfuge.
Again, I speaking as "matter of practicality", it would need a constitutional amendment. Yes, Congress could pass a law defining "subject matter thereof", but such a law would need to withstand judicial review.
Congress has MANY times tried to define freedom of speech, only to be rebuked by the Supremes. I would guess the same would happen here, hence the practical need for an amendment.