I shoot DMR and RECCE competitions and I actually never sort .223 brass by headstamp. The demand is typically for a 1-2 MOA shot at best (hardest last year was a head shot at 700Y).
Mixed brass is virtually all I shoot, and I get sub MOA performance pretty reliably.
What the mixed brass will do is put an occasional flyer out of MOA in there that you will know isn't you. By pretty reliably I mean 4 out of 5 or 8 out of 10 will hit the MOA target I am aiming at.
I argue there's not enough case capacity in a .223 to make that much of a difference compared to say, .308 where it wouldn't even be polite to openly discuss this. If you can find the middle of the accuracy node, you can tolerate mixed brass.