The .243 has much going for it. Tolerable recoil in a light rifle, combined with a flat trajectory and fine accuracy can't be overlooked. But as is often the case, folks sometimes get a might carried away with only part of the package that we call terminal performance and overlook the big picture.
To my way of thinking, the proper cartridge shouldn't be chosen by what it can do when everything goes right; its what it can do when everything goes wrong that counts. The best of us can muff a shot, the animals steps forward as the shot breaks, a gust of wind comes up, or we just plain miss because we aren't in a proper state of mind. We know how to shoot, we know where to shoot, but we misjudge the range, yank on the trigger or fail to follow through, whatever the reason is, the bullet hits too high, too low, or too far back.
Now we're faced with a crummy shot angle on a wounded animal that desperately wants to get away. The easy shot is gone, this one will be tough and the angle requires much more penetration than the broadside, so our bullet needs to perform better than it needs to on that classic broadside shot. Instead of a foot of penetration providing a killing shot, now that bullet has to penetrate a couple of feet, and in the case of a very large animal, it might have to penetrate even more and cope with heavier denser bone along its tract. The wounded game scenario differs greatly from the one where the game is rugged with a single shot that hits like a lightning bolt out of the blue.
Everyone likes to recall their successes but not so much their failures, even though we tend to learn more from our failures. A bad shot is not the fault of the cartridge or the rifle, but there seems to be little benefit in compounding a bad shot with a cartridge that can't settle matters under difficult circumstances in a reasonable fashion.
Of course the .243 could be made into a better big game cartridge, but as yet no one makes the bullet that will allow that to happen. If there was a 6mm bullet that weighed between 130-135 grs, it would have a muzzle velocity of about 2600 fps, and the combination of a moderate impact velocity with a heavy for caliber bullet that expands to about 45 caliber would put the .243 into the general purpose big game category. Despite that, there seems to be little appetite for such a bullet, or it would already be available.
Perhaps a round nose bullet with a bonded pure lead core that measures 5 calibers in length and requires a fast 1:7 twist is too far outside the normal parameters to be feasible in the eyes of the current bullet makers. Bullets that stabilize in 1:10 twists are the most popular, and after all, bullet makers have to sell their products in the real world. Certainly until recently that was the case with .22 slugs tht were made exclusively for 1:12 and 1:14 twist barrels, but it was target shooters and the military, rather than hunters, who drove the heavy .224" bullet interest.
Previously, our most popular game cartridges were available with heavy for caliber round nose bullets; the 160 gr 6.5, 175 gr 7mmm, 220 gr .308, 300 gr .375 and 500 gr .458 are such examples, and all have a reputation for being excellent performers on big game. If the 6mm bullet is to become viable in the big game arena, this is the direction it needs to take as well. It strikes me as strange that the 6mm Lee Navy of a century ago was a better big game cartridge with its 112 gr round nose bullet than the .243 is today.