I haven't really shot a .223 long range or a bolt action, but I assume like most people that wonder why others put muzzle brakes on .308's is because the lack of recoil allows you to see your own shots.
That to me is priceless. I'd love a muzzle brake on my .308.
If I go shooting myself, I see maybe 1/4 or 1/5 the shots. That means a lot of wasted ammo with no feedback.