I've never really understood the process that resulted in the selection of those commanders (including Pope). I understand that there were political considerations that Mr. Lincoln had to factor in to his decisions. But it seems to me that the Army of the Potomac had quite a few very capable corps commanders that might have made good army commanders. Hancock comes to mind, or Reynolds.
When Pope and Burnside were selected, Hancock and Reynolds were both still brigade and division commanders. Pope was selected on the basis of his success on the Mississippi, one suspects Burnside was selected simply because he wasn't McClellan or a McClellan insider.