I have exactly one place on the farm where I can shoot out to 450 yards. I've got gong now, but in the past I used milk jugs. We don't do it much, but we occasionally get set up for shooting at that distance. Believe me. It ain't that hard to get dialed in with any of our rifles. We've even done it with a Mosin Nagant.
In using it to hunt, What is going to be a problem is:
1) Learning how to read distance. We know what 450 yards is.
2) Learning how to deal with wind. I'm now putting out flags
3) Learning what your rifle and your load does
I admit that I don't have a whole lot of experience with 308 WIN. I've got one rifle in that chambering and I use it out my treestands. It is not that I wouldn't trust 308 WIN at longer distances, It just happened that I set up the rifle, a Savage 99, for that purpose. I'm sure I could make it a 400+ yard gun if I wanted to.
That one place, the 450 yard range at our farm, has another significance. It was nearing the end of one of my first deer seasons at the farm. I was coming out from an otherwise unproductive afternoon hunt. I spied a herd of doe munching out in the pasture where our 450 yard target stand now resides. I knew I wasn't going to hit anything. I just wanted to experiment to see what would happen. I did not know the exact yardage. My gun was sighted in dead-on at 50 yards. I really didn't know what I was doing in those days. I put my 30-06 against a big tree and took a shot at the closest doe, knowing that if I aimed at her chest, the round would fall well below that. I saw the bullet hit a good 7 feet below her hooves, and zip up through the grass, making some of the other doe jump. It was getting dark, and by the 3rd shot, I was mostly blinded in my right eye from the muzzle flash, and the doe were catching on that something was up and moving off. I called the experiment a success; I had proven to myself that taking a shot at that distance was foolhardy without knowing the exact distance, and attempting it without practice.
