The above is not complete. While it is true that neck turning is required when you have a sub-SAAMI minimum neck diameter in your chamber, it is also useful in standard chambers to help center the bullet during firing. This is because it removes unevenness in neck wall thickness, which introduces offset to the bullet position when the shoulder of the case has centered against the shoulder of the chamber. This happens on the firing pin drives the cartridge forward, assuming it is a rimless bottleneck case.
Two things need to be noted about the procedure: first, unless you use either a specially sized sizing die, a Lee Collett die for the neck, a bushing die for which you can choose a bushing that minimally resizes the neck, then the center neck will expand and be sized back over a greater diameter, thus causing it to need annealing more frequently. Second, after turning in neck, it must be fired once before it will be centered in the shoulder by fire forming. The exception will be if you turn the neck before resizing. That, however, will require an expanding and turning mandrel size that is not standard.
Many people who routinely turn next, do so only so far as is required for the cutter to mark the neck about two thirds of the way around its circumference. The idea is that this will center the bullet successfully by centering the majority of the next contact area. Glenn Zediker, for example, uses this method for all is service rifle ammunition. It will get the neck closer to center, but the unturned portion will still be a little thinner than the rest of the neck, and so will still full of bullet slightly off center. It just is not likely ever to be enough to matter in the service rifle match discipline. A benchrest Shooter, will not find this satisfactory, and he will have ordered a chamber with an undersize neck precisely so he may turn his next down a little further, yet not have them expand so much that they work harden excessively from resizing.
In the 1995 Precision Shooting Reloading Guide, in commenting on neck turning and other benchrest type case preparation, reported that while it was not normal to have small case changes affect accuracy greatly, he had seen one exception. He owned a 300 Winchester Magnum, that he could not get to group under about two moa, until he started turning necks. IIRC, this brought the groups down to about 3/4 moa in that particular rifle. I do not recall if he mentioned he was setting his shoulders back so that this rifle headspaced on its shoulder, or if it was still headspacing on its belt, as most 300 Winchester Magnums are loaded to do. I suspect the former.
The bottom line is that this is something that must be tested in each individual rifle to see if it makes a difference for you. If it does, and if you shoot a high volume of ammunition, you might want to consider a motorized neck turning mechanism, such as the one available for the Gracey trimmer.