"Corruptly" is an element of that offense! And it standardly involves the use of *official powers* "corruptly." Indeed for a president it's mostly what Roberts characterizes as *core* powers: fire the FBI Director, fire the AG, hold out the prospect of pardons (and then actually pardon) witnesses.
It's OK because if the president attempts a coup by executing and ransoming the families of Congress, Congress can just impeach him. And the courts can order the President to stop doing a coup 2-4 years after he's completed it.
If you can't inquire into the motive of the uses of presidential powers, you're going to have a mighty difficult time establishing "corruptly" beyond a reasonable doubt (Roberts' weaselly footnote about the public record notwithstanding).