I think you can answer your own question. The way I go about determing what killing a range that a certain cartridge/bullet combination is first to determine the minimum expanding velocity of your bullet. At that point you can plug the numbers into a ballistics calc and determine how far down range that is for your cartrdge/load velocity. Of course a bullet that does not expand will kill an animal if put into a vital area, but the chances of loosing it become a lot higher.
After determing the feasible ballistc range of your load, rifle and shot accuracy come next. For accurate 1K shots, you need and accurate rifle and load not to mention the shooter. An accurate rifle should be able to easily shoot sub 1/2 MOA @100 yds to hope for MOA accuracy @ 100yds. For an accurate load, you need consistant bullet performance and muzzle velocities. An ES of 50 fps wont cut it at 1K. You want to get it down into the lower teens or single digits or else you're firing and hoping.
Long answer short.... I do not believe the 30.06 is a 1K hunting cartridge. I have a 300 WSM
which will get 100-300 FPS more than a 30.06 and I consider it an 800-1000 yd deer/elk rifle depending on load and elevation, if the rifle and I do our parts.
Good shooting and welcome to LRH,