They could. And some have tried to over the past few years. But the bills never make it out of committee.
The key is understanding that Congress has the responsibility for establishing uniform rules of naturalization. Part of establishing those rules is identifying who doesn't need to be naturalized. Congress could do away with anchor babies with a simple piece of legislation. But they haven't.
Congress cannot legislate changes in the Constitution. For that an amendment is required.
It is by the same token that if a part of the Constitution is going to be ruled upon by the Court then it has to be a part of the arguments submitted to the Court and in the case you cite there was no arguments given to the Court on Article 2, Section 1 of the U.S. Constitution and so it was not at all ruled upon as you claimed before.