Unfortunately, it would take only one case to get to the Supreme Court to get a ruling that says all anchor babies are citizens, with Alito, Scalia and Thomas dissenting.
I really doubt that it will go that far at this point.
Expect the majority opinion being drafted by the "wise Latina." Congress should still pass a law stating what the 14th amendment is supposed to mean, but you are right that the constitutional challenge would probably succeed with the current court. In the meantime while that is litigated, what would not be challengeable would be cutting the rope to the anchor babies. Congress could change the law tomorrow preventing parents from being petitioned by U.S. citizen children if they were not either outside the U.S. or present in the U.S. in lawful status (not including visitor, student or diplomat status) at the time of the birth of the petitioning child. Who can petition, who is deemed admissible and the process for immigration is still up to Congress.