The main reason the military stays with the 5.56 is because of cost.
Whatever, if this was true we would still be flying P 51's and not spending multi million dollars on one jet. If cost was so important they wouldn't be spending billions of dollars on Research and Development of new weapons.
I am simply saying to know what your own limitations are and make an responsible shot. I could shoot a deer with a 12 ga slug from 25 yds, but if I hit it in the guts it is still going to run off. Shot placement is paramount with any round or game, big or small. If you feel comfortable with a .223 by all means use it. If you have concerns then don't use it.
As for me I have killed more deer with my .22 hornet, than I ever did with my 30.06, by the way I sold the .06, but I still have the Hornet.