You’d have to go against a precedent set in the 19th century, for an amendment made to help guarantee citizenship for freed slaves after the South failed to block the Civil Rights Act and Johnson had to step in and veto it. At this point, recodifying the jurisdiction phrase could very well require a new amendment, since the current Court is pretty divided on revisiting precedent from that long ago. And a new amendment would be a real long shot. Maybe possible depending on how next mid-terms go? But America seems stuck in a back-and-forth singsong dance when it comes to who wins Presidential elections and who does well in the following midterms.

Also, the example highlighted here about someone being born here and then moving to the country of their parents right after is just not common enough to swing electoral college votes, and a requirement for parents to have been citizens is not at all interpretable from the 14th - you would need a constitutional amendment. And it would need to address all sorts of edge cases like what happens when one parent is waiting on their green card but the other parent is a citizen with citizenship going back multiple generations.

Even though it’s a long shot, an amendment is more likely than movement purely from the courts, especially if what you want to stop is foreigners birthing children on American soil, those children spending all their lives in America, subject to her jurisdictions, and enjoying citizenship.