Targets only after 250 yards... will it kill them further??? Absolutely... will you put the animal down immediately further out??? NO. I have shot an awful lot of .223 ammo on deer and hogs. LIMIT your range, and even then, they run a LOT of the time... I will not shoot head shots over 75 yards with this caliber... not saying it will not do the job further out - it will - but your margin of error is very slim.
Targets - shoot them at any distance you choose.
We have a fair amount of pigs around. I have shot lots of them up to a bit over 250 with subsonic 22lr in the head, out to about 50 yards. Can't be much energy there.
If you have an accurate 223, and many can be really accurate, and a good enough bullet, the retained energy for a head shot should be there a fair ways out. As to longer head shots, I typically stop on heads about 300 or so yards.
Of course the other day, first time I've shot past about 250 or so in a long time, I was offered a chance at a steel wolf at 650, and the lung area was so covered with splats, I shot the head. Missed the eye by maybe an inch or so first shot.
If the energy is there, for X shot, then its only up to the shooter to know if they are capable or not.