The fed exists through its charter by Congress in the Federal Reserve Act of 1913. Clearly congress gets to define organs of government by law, no one seriously tries to make a 10th amendment case that Congress can't define organs of government.

The argument here is about independence. Can Congress define an organ of government (part of the executive branch as commonly understood) such that the president doesn't have the ability to directly administer it? Or is the president the head of all executive authority?

Similarly no one doubts that the intent of Congress was to do so here. And almost everyone thinks this has been a good thing, as macroeconomic policy can and has done terrible things in the hands of political actors in the past.

But the constitution is silent, thus the case.