Good points and well said. I am not as knowledgeable about the origin of the 375HH. If it was originally designed for shooting heavy PG at longer distances we should also remind all that at the time of its origin the typical Safari hunter would arrive with a heavy double rifle such as the 450 or 500NE for use on DG and those are not known to be a great tack drivers out past 50y let alone 100/200y, etc being limited to iron sights only in the 1920's. Same hunters might also bring a Griffin Howe 30-06 or a Mauser 7mm or 8mm rifle for smaller game and often those were iron sight only rifles as well. But marksmanship was taught in the schools and military and Springfield and Mauser rifles were capable of hitting game at longer ranges even if they may or may not have the energy to do the job way out there. Yet these intrepid hunters sometimes wanted a heavier option for the big Eland or Kudu or Wildebeest that was out of range of their big heavies. Hence the 375 was a perfect mid-bore. Perfect for Lion, Leopard, and Hippo, etc, and able to take down Eland, Zebra, Giraffe, as well.
Again in the early 20th century the bullet options were solids or softs and not much else. As bullet quality improved we got choices such as the Nosler Partition in the 1940's, and later Swift A-Frame and and Barnes X bullets in the 1980's. This enhance all rifles but greatly enhanced the capabilities of the 375. These offered both controlled expansion and deep penetration in heavy game animals. Where a 375 caliber solid was not that impressive on big game, a 300g A-Frame or TSX that expands to 2x bullet diameter is making a 3/4" hole in the game animal. That was mo-betta. Compared to the 1/2" hole from the 500 nitro loaded with solids and all of a sudden the little 375 is punching well above it intended weight class. It would not be my choice for Elephant but for most all the other DG animals it is a viable option. All that said, long range with a 375 is not 400 or 500y. It is more like 200y or a bit more. It loses too much energy much out past that.
As for dialing turrets for longer shots? If you take the time to learn how to do this and use a proper zero stop optic with reliable, quality turrets, you will be amazed how well you can shoot at distance. As a young man, the first time I fired my FAL loaded with 308 ammo at a 400y tgt I was stunned that the bullet dropped almost 2 ft! I was using a simple scope and was zeroed at 100y. That was many years ago and I have learned a lot about ballistics since that time. Today, I can dial and reliably hit 400y tgts with my 22lr 10 out of 10 shots. And that bullet is dropping something like 25 feet. So making the same shot at 400y with a 30-06, or 308 using a good FFP MIL scope is a chip shot. But that is shooting a steel tgt, not a living game animal. It is shooting from a bench or prone, not off sticks or a ruck. Practical field conditions usually limit us to taking game shots that are about half the distance we can reliably shoot targets at. My opinion.
To imply that dialing your dope risks making errors is in my opinion, a cop out. It is like saying, "I only use iron sights because them scopes might get tweaked or broken in the field". A good MIL optic will not accidentally get moved on the elevation turret, and it will repeatably return to zero in half a second when dialed back to the zero stop. Knowing when and how much to dial is a process of education, testing and practice. Ballistic apps are great but are only as good as the data you feed them. I always confirm my dope with field testing at discreate distances and then refine my ballistic inputs before I use a rifle on game. I almost never need to dial when hunting. If a critter is so far away that dialing dope might be an option, then I also will have time to range the target, dial the dope and judge the wind before making the decision to shoot. It is ALWAYS better to take the time to get closer before taking the shot. It is only ethical to limit my shots to those distances that I know I can make the shot and deliver the bullet with enough energy to expand and penetrate into and thru the vitals for the shot angle I am about to take. I do not use "Dust and Adjust" on any game animal except prairie dogs and those are varmints.
If I am glassing a game animal and am not comfortable with the shot, It is best to wait and try for a better shot.