That is because they restrict cartridges by caliber. They do not want someone using a .22LR (though I have seen deer killed with it, and always one shot). For example, the 64gr PowerPoint load in .223 will work on almost anything a .308 will, and is plenty of cartridge for deer. Bullet construction makes a difference.
To put it in perspective, we are talking differences in diameter of a few hundredths of an inch -- other factors will dominate.
Yes, but the military primarily uses an AP bullet for the .223, so you are putting a .22 hole (with a lot less energy) through a target. If it was a Partition or a something like that, not a huge problem. But the .223 is still pretty under powered compared with the .308. In Nebraska, the regulations are not on caliber but on the amount of energy the bullet has at 100 yards. Most .308 Winchester rounds will meet the requirements (900 ft pounds at 100 yards) but unless you hand load you will find few .223's that will.
I can understand partially the reason the switch was made. You can carry a lot more ammo and there is little recoil with a .223, and yes it can eliminate a target. But with military ammo, in a kill or be killed situation, I would personally choose something a lot more powerful than a .223.