Not true J Jones.
I have taken brass that has been fired many times in a trued action and a custom action and it is still not square. The cutter still took brass off the high side. THE ONLY THING THAT WILL SQUARE A CASE HEAD IS CUTTING A CASE HEAD! It will not staighten itself by being fired in a "good" gun.
As far as starting with quality brass and not worrying about it; worry about it! I just spent all day at 7mmRHB's house squaring 200 Lapua BR cases and it will shock you what I found out! That brass is probably the best out of the box brass made on this planet and out of the 200, 32 were dome shaped, 11 were dished, 4 had dimples, and the remainder (minus the 14 that were good) had a unbalanced high side!!! I might further add that the drilled flash holes still had burrs looking at them through a magnifying glass. On the plus side, there was only 1 that was .006" short in the neck, and the weight difference of the prepped cases varied only 1.2 grains! That kicks serious butt on ANY of the Winchester or Remington brass I've done.
As for the accuracy improvement, it's hard to give it a guesstimated percentage, but I honestly couldn't give a percentage to any of the benchrest techniques we all commonly do. Do you know how much difference uniforming the primer pockets does? Could you put a percentage on it? I doubt it, but we all still do it. 50 years ago, if you told someone that you were deburring flash holes, they would laugh you off the range, now it's common practice and I doubt anyone could say just exactly how much difference it makes. Maybe all or maybe nothing. On a benchrest gun it could be worth your while to square the heads, and it would do nothing to square the heads on brass to be used in an AK47.
All I'm saying is that it makes sense, and a lot of people could benefit from it if they would keep an open mind, and be willing to try something once before they say it wouldn't work. Many people poo pooed the Wright Brothers for thinking that man could fly, now who has the last laugh! /ubbthreads/images/graemlins/grin.gif