I find your comparison interesting and very much to the point. True, it could be argued that Duke knew his subjects were misbehaving (John Sutherland, IIRC, finds it ominous that he slips away and leaves another man to put things right; possibly in the hope that he would be considered "bad", and the Duke will remain "good" - ugh!); while Sir William / Mr Burchell didn't know the facts of his nephew's conduct - which Goldsmith tries to stress, BTW. Though, and here you are right again, both could prevent much if they but took trouble. So while Mr Burchell was indulging his romantic soul, Sir William was shirking his duty.