One thing I've seen happen several times with various hunters on plains game hunts is while they may shoot a .300+ magnum of whatever sort well on a typical North American hunt (which generally only involves one, or maybe 2-3 animals) they can get little weary of the recoil on a safari, where 4-6 to maybe a dozen may be taken. Some who brought a second, less powerful rifle often ended up using it more effectively as the safari went on.
This isn't always true, by any means--one of my hunting partners in RSA in 2007 used a .375 H&H throughout the 2-week safari, and another used a .338 Winchester Magnum very effectively. But quite a few do grow weary of even a .300 after several days.
