Legally, it's a trickier argument to make than some are realizing. A lot of people are arguing for the "subject to the jurisdiction thereof" approach, and advocate looking to whether or not the parents are citizens/subjects of a foreign country. The problem with this approach is that it would also exclude the children of legal resident aliens, which would run headlong into more than a century of that being accepted and completely non-controversial. Plus, perhaps political suicide.
My guess is that the SG was trying to get around the issue of saying that the children of legal aliens should not get citizenship, and that's why he focused on "reside" and "domiciled".
Two points:
If the Court gets a constitutional question wrong and then defers to that error indefinitely because of reliance, it has effectively transferred the Article V amendment power to the judiciary without going through the state ratification process.
What you call "run headlong into more than a century of that being accepted" I call relying wrongly on dicta from Wong's paragraph 93, which has no force of law, when paragraph 118 is the controlling ruling. We can't allow the Constitution to be de facto amended by simply ignoring law for a sufficient amount of time and then calling it "settled."
The governed never consented to this expansive interpretation of birthright citizenship, as there are no statutes via legislation or Supreme Court rulings that have stated this, or constitutional amendments that proposed this. Those are the normal means of consent of the governed. The tools of government that the people consented to via ratification of the Constitution were not the means where birthright citizenship for all and natural born citizen for all was determined.
Those interpretations evolved extraconstitutionally through the accretion process described in Janus: each successive actor pointing to the prior actor's behavior as authority, until the chain of reliance became long enough to be called "settled law" whether by the Court treating its own dicta as law, or by political actors treating those rulings as broader than they were.
The governed did not ratify universal birthright citizenship. They did not ratify natural born citizenship for the children of temporary visa holders or illegal entrants. Those outcomes were imposed on them, not chosen by them.
-PJ