Taking into account the physics of shotgun-type firearms and sniper-type firearms, a shotgun sniper wouldn't work.
The shotgun fires numerous bullets at one time, which would increment the spread of fire. This is why the shotgun is a close-range weapon.
The sniper fires one bullet at a time, and at a higher velocity than any other firearm. Due to the sheer speed of the bullet, it requires extreme percision as to not go off my a millimeter; which explains the scope.
When combined, you create a sniper that shoots many bullets at once, which would require more percision than the human brain can handle. It is more than 95% likely that the shooter will miss the target when using a shotgun sniper.
And that's why a shotgun sniper is stupid.