Another way to look at it is an expensive pencil barrel will almost always outshoot a cheap bull or HBAR. A barrel is accurate because it creates more consistency shot to shot. That's controlled by the quality of rifling, amount of jacket buildup, muzzle crowning, twist and number of lands, and it's length, which centers the muzzle in a low vibration point.
If the barrel material is full of inclusions and stress, just being a lot thicker isn't necessarily going to help all that much. It's just one factor of a dozen.
In the typical impossible to test comparison, two identical barrels with just an overall diameter difference will show a minor difference in accuracy. The fun part of that discussion is no one can say how much - it's never been scientifically tested and proven, just accepted. That's because the extreme benchrest shooters all use it, so it must be so. Well, a lot of that is just making the thing weigh a lot so recoil won't disturb it as much.
In the AR, so many other factors can improve accuracy that just making the barrel thick isn't even a priority - ammo, optic, and the shooter have more influence.
