It's not the gun that matters, it's the shooter.
Also "up to a point", though the shooter is the largest variable in the equation, by several orders of magnitude.
The gun matters, as does the bullet.
That super-duper 700 yard .243 VLD is a pretty thin skinned bullet, I understand ....... a close range shot would likely result in "the hickey from hell"..... the bullet disintegrating on contact.
As others mentioned about the Core-Lokts, I've had a light-for-caliber bullet come apart at close range- a .270 WIN 130gr Winchester Silvertip (it's been awhile- not sure if they even make those anymore.... I don't recall seeing them on a store shelf for at least 10 years) at about 15-20 feet.... made a wound about the size of my fist, and about as deep. Far side lung was intact ...... the deer went a good 100 yards, leaving a little blood ..... yes, he died ..... but I found him by pure chance- I was not real good at following a sparse blood trail ..... still not great at it. I've since switched to 150gr bullets- A nearly identical set-up: broadside 1 1/2 y.o. buck at 15-20 feet. The 150 gr bullet going slightly slower blew pieces of lungs out the 1" hole in the far side and sprayed them out in a nice pattern for a good 10 feet. This deer ran near 100 yards, but with every stride (or maybe each heartbeat?) there was a huge gush of blood sloshed on the ground that a blind man could not only follow, but would have to take care not to slip on and fall.......
The gun and bullet are a system.... The bullet has to be pushed fast enough to expand, and at the same time not so fast that it comes apart .... more mass helps as does modern engineering (chemically bonding the jacket to the core, Solid copper or guilding metal bullets, thicker jackets or other design elements such as dual cores (Partition/A Frame).... The bullet has to have enough mass and energy to penentrate deep enough to fatally damage vital organs..... sometimes under less than perfect circumstances.
Will a 30/30 or a .243 do that on an elk? Yes, but I think there are better choices. YMMV (and probably does).
By the same token, going to the other extreme is not good either- An 8mm Remington Magnum isn't a good elk gun, either, as the teeth rattling recoil in a gun light enough to carry all day would deter sufficient practice, at least by me.... a Barret .50 BMG is likewise overkill ... even the healthiest of us would not enjoy humping a 30 lb rifle in the high country......
But some folks like a challenge, I guess..... so if you think you can do it with a 30/30, go for it.... just don't complain when the only shot you get on your once in lifetime (or maybe it's a once in a year thing, you lucky dog) hunt is standing there quartering away at 250 yards .... a long shot for a 30/30..... a chip shot with a 7mm Mag ..... if the shooter is up to it.