The method of appointment does not affect the right of a President to fire anyone whose position is one that serves at the pleasure of the President.
Remember the controversy over who was to be the acting director of the Consumer Financial Protection Bureau (CFPB). [ English v. Trump ]
Alternative methods of filling vacancies can be legislated for various positions to take care of instances where the President chooses not to or neglects to involve himself in filling a vacancy. But once a President gets involved, it is all up to him, back up provisions are no longer relevant.