I feel we're headed for a No True Scotsman fallacy. The Trump Regime and Roberts court endorse the unitary executive theory, and they are happily overriding Article 1 powers and violating laws like the Administrative Procedures Act based on this theory's farcical and ahistorical logic.
If the theory wasn't giving him more power (like firing non-political appointees without cause or withholding funds appropriated by Congress) he wouldn't be using it.
Nobody called it a "theory" until FDR appointees ginned up a fourth branch of government in the 20th century. Then, they needed a label for what actually existed in the constitution to distinguish it from the shit they just made up. But most of the people who use the phrase "unitary executive theory" also think "emanations from penumbras" is constitutional law...
Also, the APA doesn't apply to the President, and it wouldn't be constitutional for it to do so.