Substantially for the reasons in the SG’s brief, and those I’ve discussed here previously, I think the Court will hold that the cases are (or, in the case of the refugee ban of Section 6(a), are about to be) moot.
As for whether the Court ought to vacate the decisions below: Well, the judgments below–the preliminary injunctions–have run their course, and have had (most) of their intended impact. Those injunctions (with respect to both the January and March Executive Orders) presumably have allowed numerous people to enter the United States between January and October who would otherwise have been barred by the Executive Orders. Therefore I don’t think it much matters whether the Court now “vacates” those injunctions.
Then there’s the distinct question whether the Court should also “vacate” the court of appeals’ opinions–which is, in effect, a question about whether the Court should strip those opinions of any possible precedential effect, seeing as how they won’t be erased from the history books or the Internet. Although I think the plaintiffs (and the Waxman amicus brief on behalf of Fed Courts scholars) are correct that Munsingwear vacatur is inappropriate here, I would not be at all surprised if the Court does “vacate” the opinions. Here, too, however, I don’t think anything of much practical significance turns on whether it does so or not: Contrary to the SG’s argument, this is not a case, akin to Camreta, in which the precedents would have any in terrorem effect on the President’s future conduct by increasing the prospect of damage awards. And regardless of the precedential impact of the opinions on district courts, challenges to any future entry restrictions will quickly be resolved by en banc courts of appeals and/or by the Supreme Court, none of which would be bound by the stare decisis effect of those opinions in any event.
I think, in other words, that how the Court resolves the vacatur question–along with the question, raised by the plaintiffs’ briefs, whether the Court should remand the cases or dismiss them as improvidently granted–will not be terribly significant in any practical sense.