To Kleanbore: The gun used in "To Kill a Mockingbird" is central to the plot. When used by the main character, to shoot a rabid dog, it is showing that he is not just some cerebral, high minded attorney but a practical man who is a crack shot as well. Especially in the setting of the movie, the deep south, proficiency with a rifle would be seen as a sign of manhood.
As others have stated, the sight of a gun without relevance to the plot would be a distraction and possibly cause confusion since viewers would keep waiting to see when the gun will come into play. Even a detail about a gun is only shown when it is needed to advance the plot. If you have ever seen the Coen brothers film "Blood Simple", at one point a character takes her husband's revolver, opens the cylinder, and you see several rounds (but not all chambers with a round). Late in the film the gun comes into play, and the specific number and placement of the rounds becomes key to the outcome of the action.
What might be most interesting would be a film or TV show where a key character, in the course of, lets say, taking off his coat after being at work all day, also removes a concealed handgun, placing it on a counter, or in a drawer, etc. without any further reference to it. This would show an ordinary citizen who just happens to carry a gun. If the individual were a character who is seen in a generally positive perspective, all the better.