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No surprise that you'd show up to shill for it.Your argument boils down to 'if it looks like an executive branch agency, then the Executive branch should have control over it' rather than accepting that Congress is free to set things up as it sees fit within the Constitutional constraints.
The unitary-executive crowd worships a golden calf, namely the first three words of Article 2: "The executive Power shall be vested in a President of the United States of America."
One could argue that the "executive Power" is whatever the Congress says it is. Suppose that a future Congress were to decide that the president is to be, basically, the butler for the federal government — think Mr. Carson on Downton Abbey, in charge of the household staff but still very much a servant himself — with of course the other specifically-enumerated presidential powers (read: duties) in the remainder of Article 2. It's hard to say in advance that such a hypothetical congressional action would be categorically inconsistent with the Framers' intentions.