It probably also goes a long way to making the brass more likely to take on the dimensions of the rifle in which it is shot. What I mean is this: I figured out a long time ago to keep the brass separated by lot and dedicate a lot of brass to one rifle. I'm not THAT big of a reloader, so for me that is quite workable and handy to do. When you anneal, you are softening the brass in several key dimensions that are crucial to the fit in the chamber. It also (please correct me if I'm wrong) reduces the springiness of the brass-- its desire to return to its original shape. As a result, if you fire it in a rifle after annealing, it is more likely to take on the dimensions of the rifle in which it is being fired and therefore will have an easier time conforming to those dimensions on the next loading.
Sort of, and not quite.
Work hardening doesn't change the stiffness, and so neither does annealing. What work hardening does is increase the elastic limit, aka yield stress. In other words, it takes more stress before the brass starts to undergo plastic deformation. At the same time, it tends to reduce how much strain the brass can tolerate before failing.
If you start with annealed necks, they'll expand elastically until they reach their YS, and unless they are a fairly close fit in the chamber they'll then deform plastically to fit the chamber the first time they are fired. The elastic deformation will be recovered as the pressure drops after firing, so you always end up with a bit of clearance afterwards.
If you had a work hardened case it will also deform, and if there's enough room the sort of stress applied in firing will have it deform plastically as well - the stresses at play will well exceed the YS - though it might fail before expanding sufficiently if the brass is brittle and the clearance too great. It will have somewhat more elastic deformation recovered after firing too.
If you then only neck size, the rest of the case will not undergo further plastic deformation if you fire it in the same chamber. It will expand on firing to meet the chamber walls, but that expansion will be within the elastic limit and will be recovered as the pressure drops, so there'll always be some clearance. It will only be the neck that undergoes cold working, and will need annealing every so often, because of the fact that you are sizing it.
