Here's the exact quote from JOC regarding why he's seen more animals killed with the 7x57:

"Yet I think I have seen more game killed with fewer shots from this modest little cartridge than with any other. The explanation for its deadly efficiency does not lie in blinding velocity, in big bullets, in a frightening number of foot pounds of energy. It lies in the light recoil, coupled with the excellent hunting accuracy of so many 7×57s. Those who use it are not afraid of it and, as a consequence, they tend to shoot it well—and to place their shots well. In case no one has told you, the most important factor in killing power is putting that bullet in the right spot."

That is from this article: https://gundigest.com/more/classic-guns/forty-years-little-7mm

As JB and lots of others have mentioned, it all boils down to not being afraid of the cartridge (i.e. recoil, muzzle blast, etc.), and with today's bullets it's arguable whether or not a "Loud-n-Boomer" is even necessary for the majority of game most of us hunt. Now, if someone "wants" to hunt and shoot his L-n-B, that's an entirely different issue.

"An archer sees how far he can be from a target and still hit it, a bowhunter sees how close he can get before he shoots." It is certainly easy to use that same line of thinking with firearms. -- Unknown