President Trump purported to fire Lisa Cook, a member of the Federal Reserve Board, for cause. Here, at least, Trump is not asserting an absolute removal power over the Fed. Wilcox said in dicta the Fed was different than the FTC. And I think under the Solicitor General's position in CASA, the federal government would bind itself to the Supreme Court's holdings, as well as reasoning. I'm not sure how that analysis maps on the flag-burning executive order, but that is a topic for another time.
There is an angle of Cook's firing that has not gotten much attention. The alleged cause to remove Cook is that she falsified terms on a mortgage. And who made that allegation? Bill Pulte. Who is Bill Pulte you might ask? The Director of the Federal Housing Finance Agency (FHFA).
That agency should sound familiar. The FHFA was headed by a single director who served a five year term, and could only be removed for cause. Collins v. Yellen (2021) held that the structure of the FHFA was unconstitutional.
