I haven't loaded my own for years . . Don't have the time nor the patience anymore . .
But I buy my reloads from one specific guy who's been buying fired .223 (5.56) brass from the Army at Ft. Carson. He uses two tumblers, and the first clean is with a medium media and the second is with baking soda . . He resizes and de-primes before the last cleaning cycle . .
On the dirty primer pockets, one of two things, in my experience. Cheap primers or really high pressure loads . . Usta shoot a .300 weatherby with max loads, you know, slow burning firewood, and those were the dirtiest cartridges I've ever seen, the cases were full of crud, the primer pockets needed scraping, not just brushing. Don't do that anymore, neither my budget or my body will tolerate it . .
My Loader also claims annealing isn't really needed on DoD standard ammo because they don't get the pressures needed to actually work harden the shoulders . . I run a lot of it through a SS Mini 14 (1st Gen) and haven't had any problems. They feed good and I don't get hangers or split cases . . so he must be doing something(s) right.
He does anneal anything that'll be used for more than a standard DoD spec. load where higher pressures are going to be used . . Y'know, varmit loads and heavier bullets, etc . . I've had him load stuff for my Swift and the .243 and, again, I haven't had any problems with either bad cases or flyers . .