I see we are trying to psychologically break this down
I would say it has to do with more room, better view, and pride
You know what a stagecoach is, yeah? Basically a horse-drawn carriage for transporting people, for a fee. The original taxi, if you will. 'Round the days of the Wild West, when firearms and ammo were readily available if you could afford, highwaymen and gangs were becoming more and more common, as well as hostile Native American tribes in certain areas. Stagecoaches couldn't afford to travel without a shootist for protection. Shooting from a fast-moving vehicle is no easy feat however, so rifles and pistols weren't smart to rely on for stagecoach protection, so the guy sitting next to the driver would often have a loaded shotgun (with some form of scattershot, obviously) at the ready, what with shotguns not needing precise aim. That's where the term originates from.
No, its a monkey see monkey do situation. They weren't born knowing of shotgun. They saw it in the media and simply follow suit like the blind masses they are. Applicable to many other things as well.