up to 1km is into the heavy 5.56 or average optimized .308 territory for distance shooting assuming you're just hitting paper and aren't shooting for points it's more about your rifle and your ability to dial in your environment than it is the cartridge. if you're shooting for points at these ranges or trying for steel challenge, you'll want to "upgrade".
that being said, 7mm Winchester short magnum, .300 Winchester magnum, .300 Norma magnum, and .338 Winchester magnum are "good out to a mile" if the shooter is consistent and the rifle has a quality set up. 6.5 Creedmoor is much more ballistically stable than 5.56 or .308 at these distances as well, but on the shorter end of the scale and has the happy advantage of being AR-friendly. the cross-sectional external ballistics of the bullets, stability in flight, is usually only important if your environment is the limiting factor rather than cartridge - you have get top quality G7 bullets to roll your own loads for nearly any cartridge you want. when people want to use a different cartridge for this specific task they're usually wanting hand load headroom in the cartridge capacity for bullet selection or a more out-of-the-box solution that's easier to dial in than weeks of hand-loading and testing.
for what it's worth, for up to 1km where i am (elevation, latitude), i use either 7mm-08 or .300 WM. with .300 WM being my "long range" cartridge of choice with a 208gr Hornady AMAX on top of 775gr of H1000. Sierra 175gr on something like 64gr of IMR4831 would be quite gentle, but stout at 1km.