If more power than the 5.56 is needed, sure, you can move up to .308. But, that is exactly the point - a .308 rifle is also two pounds heavier to handle the power, cartridge length, and recoil.
The mililtary decided .308 was too much, and unnecessary in combat out to 500m. Downsizing meant they could increase the ammo load of the soldier another two pounds, plus he'd shoot it more often and more accurately because recoil was half. For combat, more bullets in the air means more hits, and that means the enemy can't fight as effectively.
For American hunters, moving up to an alternate caliber means they get 40% more power, reducing lost game and being more ethical hunters. It makes the AR15 a medium game rifle, and deer hunting is America's #1 game animal. In some states, it means the gun is legal, whereas 5.56 would have got them, the gun, their vehicle, and their wallet jail time.
Hunting with an AR, as opposed to the .30-30 lever? Its more accurate, has more range, more power down range in an alternate caliber, is easier and safer to load and unload, doesn't force you to chamber every round and nick up the ogives unloading, allows any optic to be mounted on a secure rail directly over the action, is more durable, takes less maintenance, and much more weatherproof. Take an AR out in freezing rain, and you don't even have to wipe it down at the end of the day, the stock won't swell or anodizing rust. Neglect a lever action like that and it may not even function the next day.
AR's and alternate calibers work just fine, we have good reason to use them. My 6.8SPC dissipator has a long life ahead of it, and I can find ammo on the shelf at Academy, even in SW Missouri.
BTW, it reopens in a couple of weeks, not bad for being completely destroyed last May.