Actually, for more decades than the .458WM has been around, THE issued rifle for 99.9% of African game departments was the .404 Jeffrey.
The .458WM is a Johnny-Come-Lately round to the African hunting scene.
The default load for Jeffery's .404 was a 400grn/.423-dia RN bullet @ 2050-2100fps. Despite that rather tame velocity, it made its reputation by killing the Big Bad stuff right now, out of all disproportion to its "paper ballistics."
More importantly, for a .400-class cartridge the .404 imparted relatively mild felt-recoil, no worse than a .375H&H with 300grn loads. That's why it proved so popular with Game Dept personnel, staffed generally by skinny, underfed, indigenous tribe folks.
In his book on African rifles and cartridges, "Pondoro" Taylor cites the Jeff .404 as being "the elephant gun" in his time there, but also for rhinos, hippos, and lions. He also noted that most complaints about "stopping power" were due to either poor bullet-construction (a common problem back then) or poorly placed shots, not lack of velocity.
It was only in the early 2000s, when CZ was offering its 550-based Magnum rifles chambered for a variety of African cartridges, including the .404, that Hornady decided - for no good reason - to increase the velocity of its .404 ammo 250-fps faster than the original load with a 400grn bullet. Right up there with the 416s, like the Rigby.
It also needlessly increased felt-recoil.
Ask me how I know. 
When down-loaded to its original specs with Hornady's RN or SP bullets (or any other modern high-quality .423 bullet), the .404 in my view is still the best of the .400-class of African DG cartridges.
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