Lots of people shoot Service Rifle and Match Rifle matches at 1000 yards.
That's ARs, M14s (M1A), and Garand's Then there are Match Rifles, Any Rifle-Iron sights.
I've shot all three, my best 1000 yard scores I've shot, shooting for the AK NG was with the M1A.
For info: The X-10 Ring on the NRA HP 1000 yard target is 20 inches in diameter or about 2 MOA.
Besides the environment (wind, mirage, etc) its about seeing your target.
So in HP they increase the size of the black aiming circle. For example on the 200 yard target, the X-10-9 rings are black. At 300 the 8 ring is also black and at 1000 the 7 ring is black too.
So the black bullseye looks about the same size setting on your front sight.
Like any other shooting, how well you shoot at distance is related to how much practice you do.