I have always used a .300 Win Mag. Note that Mr. Hawks says the .30-06 can shoot anything in the relevant class of game, so there is no need for the .300 win mag, which delivers more punch than you need along with more recoil.
If you don't find the recoil of a .300 a problem (and I don't, though I don't like anything above a .416 Rigby, and then only in a well balanced gun), then you have added stopping power, at no real cost to you. And I have found - through many safaris - that I can always use more stopping power.
Let's go to the bigger calibers for a second. A .375 is legal on elephant. And it will kill an elephant (I and many others have done it). So why would you go up from there? By Chuck Hawks' analysis, you get no more killing power with the larger calibers, but you get more recoil. So they have no reason to exist. Why then would you use them? Because - in my opinion - there is a bit greater margin of error with the bigger calibers, and while they just do the same job, they do it better. Same analysis applies to the .300 magnums.
So if you aren't recoil sensitive, shoot the largest caliber you like and can shoot well, within the range of what's suitable for what you're trying to kill. I think if you analyze what Mr. Hawks says, it really comes down to that.