Untold thousands of safari hunters experience probably disagrees.

As for the .416 being an all-rounder including on plains game, I wonder how the average safari client fares on accurate plains game with .416 recoil? Clients bragging expert tales are often are far different from their PHs experience with the same. Those missed kudu at 30 yards evaporate! I think the recoil of a .416 for plains game shots is too much for the average whitetail stand hunter. The reason the .375 shines as an all-rounder. Recoil is still stout but milder. As for buffalo, guys like Harry Manners shot thousands of buffalo with a .375 in Mozambique. For close thick cover hunting I'd turn to a .450 or bigger in a double rifle anyway.

They all do the job. Only the law prevents the good old buffalo killing .318 WR also being used.