Why do people think this Supreme Court--which is mostly conservative--absolutely will not choose to review a case if it comes before them? That's like thinking the last word on abortion from the Supreme Court was uttered in 1972.
This is obviously a reference to Roe v. Wade. But the thing about Roe v. Wade is that it was not only controversial at the time, it
stayed controversial. From 1972 (when Roe v. Wade was issued) until 2022 (Dobbs v. Jackson overturning it), there was always
at least one Supreme Court justice who was openly urging in their opinions for the decision to be overturned. The original decision had attracted a lot of criticism in the legal field, even from some who were politically inclined to agree with it. Akhil Amar, for example, is politically liberal and pro-choice but was very critical of the decision (having listened to some episodes of his podcast, what seem to be his "go-to" cases where he thinks the Supreme Court just made stuff up are Dred Scott v. Sandford, Roe v. Wade, and Trump v. United States (the immunity case)).
This sort of thing applies to other cases that were overturned. The most recent "big" overturn was Loper Bright overturning Chevron. But Chevron had attracted a bunch of criticism prior, there had been some hostility towards it shown by at least some justices, and it had become practically a dead letter by the Supreme Court already.
Or for an older example but one where the overturn happened quickly, let's consider the surprisingly fast reverse of Gobitis. Minersville School District v. Gobitis (1940), saying schools could force kids to salute the flag even if they considered it against their religion, which was then overturned in in West Virginia State Board of Education v. Barnette (1943). In between those cases, there grew considerable opposition to the first, on and off the court.
Three of the justices in the majority of Gobitis stated in the opinion of an intervening case (Jones v. City of Opelika (1942)) that they regretted their votes in the original case and they wanted to overturn it. Between that and two of the justices who were in the original majority retiring and being replaced, what was an 8-1 decision was turned into a 6-3 decision the other way. But again, we saw signs the court was interested in overturning it (they had four guaranteed votes to do so, with the dissenter in the original case plus the three who said they changed their minds).
None of this is the case with United States v. Wong Kim Ark. I don't think
any justice since the decision has called it into question, explicitly or implicitly (to be fair, there hasn't been nearly as many opportunities as there was for something like abortion--but still). Nor has there been that much of a groundswell legally to overturn it. Yeah, you can find some people in the legal field critical of it, but they tend to be more on the fringe. The vast majority of commenters I've seen on it--and this includes those of the more conservative variety--have
I'd also argue that the arguments against children of illegal or temporary immigrants gaining citizenship under the Fourteenth Amendment are very weak--but if they cared about what
I thought were weak arguments, they wouldn't have ruled the way they did in Trump v. United States (the immunity case). Still, I'd say the arguments here are worse than that (not only on the merits, but also on the question of stare decisis: At least Trump v. United States wasn't overturning any prior decision).
But laying aside the question of the merits, for the aforementioned reason there's not much reason to think the Supreme Court would be willing to overturn an old precedent like this given the lack of impetus for it.
Of course, one doesn't necessarily need an overturn of Wong Kim Ark. A tactic one will often see by those who assert that the Citizenship Clause doesn't apply to the children of illegal immigrants (or go further like the executive order does and also deny it to the children of people who aren't permanent residents) is to say Wong Kim Ark doesn't apply, as the case was concerning the son of two legal permanent residents, and therefore does not apply to non-citizens who aren't legal permanent residents. Thus, they argue, the decision doesn't need to be overturned, just distinguished. It is technically true the case was concerning the son of legal permanent residents, but if one reads the
reasoning of the case, it's hard to see how it wouldn't apply beyond that. The response to that is to say it's just dicta, but the "dicta" in question is the whole reasoning for the decision, so that's a bit of a weak attempt; it's not some side comment in a case we're talking about here, it's the whole reasoning for the decision.
To some extent, though, I'm actually appreciative of the executive order, because I would like to see this issue cleared up more officially by a court.