Its shooter problem more than a caliber problem.
You simply can't make accurate first round hits like this at 875 yards unless you know what you're doing. Knowing your rig and how your round relates to it and obviously solid marksmanship fundamentals.
Most hunters are afraid to shoot over 200 yards frankly because they don't know their rigs well. They hide this lack of knowledge and experience behind "its not ethical".
When you have the training to make hits like this you know the "ethical" argument is BS.
I'm not knocking guys who know their limitations, thats a good thing. But don't point fingers with the ethical statements because you can't hit a house past 200.
The OP can learn how to do this with a .308 too, just gotta really learn your stuff which means putting in the time and being honest about your abilities.