I saw a test where a guy shot groups with all identical brass and then groups with as many different head stamps mixed as possible. The mixed groups actually were slightly tighter on average than the single batch of brass.
Edit. Found it.
https://www.gunsamerica.com/digest/reloading-science-do-you-really-need-to-sort-your-brass/
This example is with a commercial, off the shelf grade chamber, in an AR15. The tolerances are usually quite generous. Therefore there wouldn't be much difference in accuracy. Not only that, the cases would have been full length resized, which in most cases isn't conducive to good accuracy.
When you're loading for a rifle with a tight match chamber or even a bolt action, hunting rifle, case consistency can make a very noticeable difference in accuracy.
One of the main differences, is that many folks only partially resize their cases or just the necks when they're going for accuracy.
Some people turn down the necks to get consistent tension on the bullet. I've never found this to be beneficial in an off the shelf rifle, other than it eliminates one more inconsistency. The neck areas of the chamber are already generous and this practice just allows for more expansion while firing.
When a custom chamber is involved, everything is tighter, some won't even accept factory ammunition. In this case, neck turning actually shows positive results, as does precision trimming to length.
Weighing brass can have beneficial results as well, even with factory chambers, but only if the shooter is fire forming the cases for use in a specific rifle and partial or neck resizing only.