I feel your pain. But as a lawprof who teaches Chadha every year, I've got to observe that the idea that there are 3 defined categories was controversial and fought over in that case. Read Justice White's dissenting opinion:
[T]he wisdom of the Framers was to anticipate that the Nation would grow and new problems of governance would require different solutions. Accordingly, our Federal Government was intentionally chartered with the flexibility to respond to contemporary needs without losing sight of fundamental democratic principles. This was the spirit in which Justice Jackson penned his influential concurrence in the Steel Seizure Case:Burger had to protest that he was not relying on "empty formalities." I'll bet most law professors teaching separation of powers present Jackson in a much better light than Burger.
"The actual art of governing under our Constitution does not and cannot conform to judicial definitions of the power of any of its branches based on isolated clauses or even single Articles torn from context. While the Constitution diffuses power the better to secure liberty, it also contemplates that practice will integrate the dispersed powers into a workable government."Youngstown Sheet & Tube Co. v. Sawyer, 343 U. S. 579, 343 U. S. 635 (1952).
The idea that are "three defined categories" of power is not too obvious to require support from case law. The case law itself shows that.