You can kill just about anything out there with a .22 as long as bullet placement is precise, and the critter cooperates and stands stone still while you get a chance to set up, calm down, take careful aim (remember, proper breathing) and squeeeeeeze that trigger until the shot goes off unexpectedly. Assuming of course that your rifle will place it's payload precisely where you aim at.
Yes, a .243 will kill an elk. So will a .270, and a host of other cartridges will too. But in the world of Murphy, I'd rather have something that's gonna be sure to do the job without taking a chance on wounding the animal and it getting away. That said, I still believe that 180 grain bullets from a 30.06 is bare minimum for Elk. .308 is good, but won't have the same energy levels at distance as the .06. I want something that's gonna bust whatever slabside rib gets in the way, penetrates both lungs (at a minimum, hopefully catch the heart too), and bust the off side shoulder at up to 200 yards, so he don't run into the next state.
This is just my opinion as I've not found the perfect conditions, as stated in the first paragraph, in all the years I've been hunting. So please don't take it as a attack on your personal choices. Only you can attest to what has happened in the past, and only you can justify what cartridge you choose.