I don't think a recreational sport hunter needs anything bigger then a 375HH for hunting anyplace on earth or for any species. The 375HH with a good bullet and scope with the bullet place in a good spot will kill anything alive with little effort. I have seen countless big animals killed and many crumpled in their tracks with the 375HH. I know of one man who has killed 81 cape buffalo with a 375HH and never lost one. Another who has shot 16 lions, and hippo, elephant, rhino, all with the 375HH he has been a professional hunter for over 20 years and swears by the 375HH. The list could go on but you see it has an impressive track record
It's easy to shoot and works as well on the smaller steenbok and the longer 300 yard shots as well. It's easy enough to shoot that I passed my Shooting exam for my PH license with my 375HH. It's low recoil and sufficient power make it the rifle to have on any safari.
Sure there are those limited folks who seem to have a big voice in the way things should be done. They will say the big 500 A2 or some enormous Weatherby should be used to hunt the big 5. Those rifles are not hunting rifles in my opinion they are backup rifles. One needs to define the difference before they spend the money for a gun they may shoot 5 times while hunting. If they have such great wealth that it's not relevent and they want a big bore for the gun case then that's fine. My guess is 99% of the bolt and double guns 458 and bigger in the USA will never shoot anything they were designed for.
I have a 458 Lott and have never once used it for hunting in the USA or Africa. It's my backup rifle for my job. I don't hunt with it. For hunting I would use my scoped 375HH every time. I suppose there are areas of thick bush where the Lott would be better and would be chosen in those limited situations. Just because I have it not because I absolutely need it.
As far as what is needed to hunt plains game. My personal opinion after seeing likely over 1000 aniumals shot is 30 caliber or bigger. I don't prefer smaller then 30 caliber rifles. Sure they will kill but the finding is the problem. Sub 30 caliber bore diameter leave limited blood trails and blood trails are critical with herd animals, and with the hot sun which will dry out the few spec's of blood typically left by game from smaller bores.
When all goes perfect sub 30 calibers are fine but if anything goes wrong at all they are not a good choice. The majority of game shot in Africa will be quartering away from you at the shot. That makes exits very unlikely unless your shooting an X bullet or a bigger more powerful rifle.
The majority of hunters from America bring a 30 caliber magnum. They work nicely and when using 180 or 200 grain bullets usually shoot though most game with little tracking and sufficient blood trails. The 338 is a leap forward and much better then the 300 magnum. The 358 Norma and the 375HH are at the top of the recreational sportsman list of preferred guns in my opinion.
I have had plenty of guys with 270, 280, 7mm, all work nice and will kill game. They don't provide the margin of blood trail I like. I would take a hunter with any gun or weapon he has or likes. Bow, handgun, spear, I don't care. I'm not suggesting it's 30 caliber or stay home. I'm suggesting what I have seen as a truely good functional minimum bore size.
Am I opinionated on this....You bet I am. It's no fun watching a hunter at the evening meal who has a long face and depressed look when the others are laughing and having a wonderful time and experience. I have to be a professional hunter and a therapist to help the man who has lost his game enjoy his trip. It's an aweful feeling to come back to camp and see 5 other hunters laughing and having the time of their life when one man who has lost game is so sad. Most guys plan the trip like this for years and spend only ten days doing the hunt. Why should any of them have it ruined because of one problem like this? Especially when it's so easily solved by bringing the right gun from the start.
Remember this is not fishing where the challange is to land the biggest fish on the lightest line. When travelling that far and spending your long time savings for a trip, bring the right gun!