I tend to run high pressure loads in my 223 rifles. I've unscientifically annealed many rounds. Figure 15K a year since about 1990. Never had a failure and the brass always shoots just fine. Of course I may just be waiting for a problem, but not really as the case head never gets too hot by holding it in my fingers. As to neck tensions-- I would have guessed that also. But by feel they are more uniform. And FWIW once the brass would get work hardened(4-5 firings) it would not shoot as well and there were many differences in the feel of seating each bullet. Anneal the brass and accuracy was back and the seating was much smoother and more consistent feeling..
Get as close as you can, but utilize your skills as needed.