The mistake that the Supreme Court makes is to presume that the answer to this specific question must be found in the Constitution.
Could executive branch agencies be turned into helpful adjuncts to federal courts without usurping judicial power? Yes they could.
Ilan Wurman is a Visiting Assistant Professor at the Sandra Day O’Connor College of Law at Arizona State University, where he teaches administrative law and constitutional law. He is the author of A Debt Against the Living: An Introduction to Originalism (Cambridge University Press, 2017).