There is no way in hell the founders thought a president could unilaterally disassemble an entire agency that was explicitly empowered by Congress. Thomas Jefferson didn't want to buy ships. He didn't try to disband the Navy. And it's possible the SC would have stopped him if Congress had the will. There is not a long history of impoundment being a major tool of executive authority. When Nixon tried to shut down multiple programs within an agency, he was shot down in court and Congress passed a law delineating exactly what he could and could not do. There is no reason to think that law runs afoul of the Constitution. Article 1 does not grant any right to impoundment. The actions of past presidents aren't precedent or else (in the case of Jefferson) we'd still have slavery.

If you disagree, please type the words: "The President can unilaterally disband a federal agency empowered by Congress whenever he wants for whatever reason he wants and no one can stop him". Because that is what you are implying.