Getting into shotgun range effectively puts into melee range of your target as well as completely out of cover which makes you vulnerable to every other enemy as well.
Meaning shotguns carry more risk to use effectively than any other weapon. Now combine that risk with a low damage output (compared to fusion rifles and sniper rifles) and there isn't any point to use them other than for fun. Which in my opinion shotguns are incredibly fun to use in pve
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You, sir. You get it.
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Yep, I use them a lot because they are just fun to use. They aren't really practical.