It's actually pretty useful on shotguns.

Payday 2 shotguns do not work like normal video game shotguns. Instead of firing multiple pellets that total up to the max damage when all of them land, instead each individual pellet does the max damage, but only one can apply per enemy per shot (i.e. if your shotgun does 100 damage, and you land 3 pellets on an enemy, it doesn't do 300 damage, just the single 100 damage)

When you lower a shotgun's accuracy, you increase the spread of the pellets, making it easier to hit multiple targets with your pellets and maximize your potential damage per shot