I think putting this at the feet of the genius of the English/American Common Law is misguided. There seems to be plenty of precedent for providing due process protections for established, naturalized aliens, which should otherwise guide a precedent-respecting common law court.

From Cornell's gloss on the Court's gloss of the Constitution's treatment of Aliens w/in the US:

In various opinions, the Court has suggested that at least some of the constitutional protections to which an alien is entitled may turn upon whether the alien has been admitted into the United States or developed substantial ties to this country.

See Dep’t of Homeland Sec. v. Thuraissigiam, No. 19-161, slip op. at 2 (U.S. June 25, 2020) (stating that “aliens who have established connections in this country have due process rights in deportation proceedings” ); United States v. Verdugo-Urquidez, 494 U.S. 259, 271 (1990) ( “These cases, however, establish only that aliens receive constitutional protections when they have come within the territory of the United States and developed substantial connections with this country.” ); Landon, 459 U.S. at 32 ( “[O]nce an alien gains admission to our country and begins to develop the ties that go with permanent residence his constitutional status changes accordingly.” ); Kwong Hai Chew, 344 U.S. at 596 n.5 ( “But once an alien lawfully enters and resides in this country he becomes invested with the rights guaranteed by the Constitution to all people within our borders.” ); Johnson v. Eisentrager, 339 U.S. 763, 770 (1950) ( “The alien, to whom the United States has been traditionally hospitable, has been accorded a generous and ascending scale of rights as he increases his identity with our society.” ); Yamataya v. Fisher, 189 U.S. 86, 101 (1903) ( “[I]t is not competent for the Secretary of the Treasury or any executive officer, at any time within the year limited by the statute, arbitrarily to cause an alien who has entered the country, and has become subject in all respects to its jurisdiction, and a part of its population, although alleged to be illegally here, to be taken into custody and deported without giving him all opportunity to be heard upon the questions involving his right to be and remain in the United States.” ).

My intuition is that even if the due process rights recognized above were read narrowly by the Court to be procedural rather than substantive, I think in a practical terms this would make an undertaking of denaturalizing and removing established American aliens prohibitively costly (it just would not be practical to provide sufficiently fair process for millions of people).

I'm not saying that Trump/Miller won't be able to do this. But they will be able to because the Court, with its jurisprudential drift towards natural law- inflected Originalist interpretation, has and will be abandoning stare decisis (see Dobbs, overruling Casey, which, other than being the abortion case, was the Court's articulation of its own stare decisis guardrails) and will be looking at cases, when it sees fit, as a matter of first impression. This is an abandonment common law principles, a terrible devolution towards continental, "civil" law barbarity.