Congress just spent the last 90 minutes reading the entire Constitution. Wouldn’t it be cool if the Supreme Court did the same at the start of their term? Just think, Justice Thomas would speak from the bench! I imagine Justice Scalia would read the Second Amendment, and Justice Breyer would roll his eyes. And, we can get some pyrotechnic special effects to illustrate the penumbras emanating from the Bill of Rights! Hopefully the Court won’t skip over the Privileges or Immunities Clause. That would be fun.
Could Congress constitutionally mandate that by statute? Doubtful. Or better yet, could Congress mandate that the Court cite a specific provision of the Constitution when writing an opinion? No way in hell.