The thing to remember here is that a standard suppressor is held true to the bore usually at the very least by a thread and shoulder or two point contact bush style and exit hole is no more than 6inches from the muzzle an requires at least 1mm clearance on projectile.
suppressor built into the shotgun barrel could be 16? inches from the muzzle of the insert whicvh is ratteling around in the shotgun chamber and will likely never be in the same place twice.
It would be like trying to shoot 243 ammo threw a 308 rifle with no sights and expecting all shots to go threw a 7mm hole 16 inches away without touching the sides of the hole.
Not saying it cant be done but would require lots and lots of clearance, a small suppressor on the insert itself would be the best option for getting everything aligned and you could possibly add a BIG clearance washer at the end of shotgun barrel could work okish, basically twin chambers.
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