You can build a .416 Rigby or even a .585 Nyati on a standard '98. Doesn't mean it's the best idea even if Rigby did it.
The .400H&H neck is too long for 400gr bullets. You could not seat the bullet flush with base of the neck. Sure it should cycle very slick but it loses case capacity and will need higher pressure to equal a .416 Rem. So the Rem can be loaded at lower pressures and equal the .400 just like the Rigby will reach Rem velocities at lower pressures.
Efficiency can be found in cases with fatter bodies like the .404. This is why a .300WSM can equal the velocity and energy of a .300 Win mag with less powder. This is not the case with the .400H&H which uses the same basic case as the .416 Rem. The Rem is more like a blown out .400. My .300 H&H cannot come close to the .300WBY mag but the blown out Wby will equal H&H ballistics at much lower pressures.

The .465H&H is a different animal. The long neck allows the 480gr bullet to seat deep in the .460 Wby based case to give a COL of 3.5", more suitable to a '98 Mauser action. At 2375fps ( H&H ballistics)
it gives Lott performance with lower pressures. A classic with an advantage.

H&H Big Bores
.375 .400 .465