It is black letter law that the Supreme Court's original jurisdiction is fixed by the Constitution. By contrast, Congress can regulate the Supreme Court's appellate jurisdiction. As a result, a litigant cannot simply file an action in the Supreme Court to demand relief. Poor William Marbury learned this lesson the hard way more than two centuries ago.
I thought this much was clear, but apparently not. The Supreme Court's statement in A.A.R.P. v. Trump violated Marbury v. Madison. (I cannot call the statement an order or decision, because the Court was without jurisdiction.) When the Justices voted, the District Court had not issued a ruling and the Fifth Circuit ruled it had nothing to review. There was no credible allegation that the lower courts were dragging their feet. Indeed, both lower courts were moving with remarkable dispatch. Judge Ramirez's concurrence explains why there was no "effective denial of injunctive relief based on the district court's failure to issue the requested ruling within 42 minutes." As a result, there was no actual lower court decision for the Fifth Circuit to review, and no lower court decision for the Supreme Court to review. The proper order, if any, was to deny the application on the expectation that the lower courts would move promptly. The Court has done that from time to time. But I cannot recall the Supreme Court issuing a global injunction against the executive branch while the lower court was in the midst of deciding the issue.
The short per curiam order cited the All Writs Act. To be sure, courts can take actions to protect their jurisdiction. But they have to have some jurisdiction in the first place. The Supreme Court had no appellate jurisdiction. The Supreme Court can only exercise appellate jurisdiction when there is some ruling of the lower court. Here, the Supreme Court directly reviewed the government's actions. Cutter v. Wilkinson (2005) explains that SCOTUS is a "court of review, not of first view." No judge had ruled on the merits when the Supreme Court enjoined the government. This case threw Cutter to the wind. Can you imagine if the Supreme Court had bypassed all lower courts, and enjoined an emergency COVID regulation twenty-four hours after a district court TRO was filed? Worse still, the Court did not actually grant the ACLU's emergency application. This is part of a disturbing pattern of playing games with nomenclature. The Court simply issued an ex parte order against the executive branch in its original jurisdiction.