There’s a simple answer to the Anchor Baby issue, that doesn’t require an amendment to the Constitution.
Simply treat undocumented immigrants the same as visitors who have arrived on a Visa - any children born to a Visaholder legally is a citizen of the state of origin of its parent(s), and cannot obtain a Birth Certificate here (they have to visit their respective foreign consulate for that).
All this requires is an added classification to existing rules, of a traveller “without a Visa” and to extend the same existing restrictions to them.
Yes, but it will never happen because there is a benefit to those who make the laws to continue to have anchor babies pouring over the border.