Judge Kathryn Mizelle of the Middle District of Florida issued an opinion finding that the "set aside" remedy under the APA is (likely) unconstitutional. Here is an excerpt from the opinion:

Even if Congress were to enact a law clearly empowering Article III courts to vacate agency rules or regulations and automatically cause their erasure from the Code of Federal Regulations, vacatur would likely still be inconsistent with the limited nature of the judicial power and the non-delegability of core legislative power to the judiciary. As a result, I doubt any amount of tradition, practice, or lower-court liquidation can correct the constitutional infirmities of vacatur as currently understood. Because I am not aware of any court to have addressed the constitutional dimensions of vacatur as opposed to its statutory basis, and I have only gestured at them in the past, see K. Mizelle, To Vacate or Not to Vacate, at 19–20, I explain my doubts in full. First, I address why vacatur, if considered an equitable remedy, likely transgresses Article III's grant of judicial power because it has no Founding-era analogue and does not comport with traditional principles of equity. Second, I explain why vacatur, if considered a legal remedy, presents serious separation-of-powers problems. Third, I address why vacatur, when analogized to appellate review, still fails to cure those significant separation-of-powers issues. Finally, I conclude that, consistent with the Constitution, "set aside" in Section 706 is best read as a rule of decision when applied to agency rules.

This is an issue that does not neatly divide the Court along right-left lines. Chief Justice Roberts and Justice Kavanaugh, both alumni of the D.C. Circuit, want nothing to do with this argument. Justice Gorsuch, who never met a regulation he liked, wants to eliminate vacatur. Justice Barrett tabled the issue in CASA, but I suspect she leans with Roberts and Kavanaugh. This opinion will go up on appeal very soon.