Weatherby has developed a poor reputation in some circles in Africa - and the MK-V rifle also gets a lot of criticism regardless of chambering. African professionals in general don't get all googly eyed over high velocity the way we do here. Ideally, with a suitable caliber and bullet weight, 2400 fps seems to be the velocity aspired to in many of the newer African game cartridges. This velocity gives a reasonable trajectory to 200 yards, and with practice to 300. Although there are exceptions most African game is shot closer than 150. More importantly, 2400 fps assures good bullet performance. Game which is sensitive to bullet shock would be good candidates for the .378, and the lion comes to mind in this regard, and Ross Siegfried speaks very highly of the .378 for use on lion.
From my own perspective, I shoot the .375 Ultra, and when I began planning my Tanzanian buffalo hunt I settled on the 380 gr Rhino as the bullet I wanted to use. Shooting over a chronograph, I found that my loads would consistently give me just a smidgen over 2300 fps. For use in Africa, a .378 loaded with this bullet could easily hit the magical 2400 mark. With lighter bullets - like the 300 gr TSX - loaded to 3000 fps, the .378 would be deadly on the large antelope like eland, and with a light soft-point loaded to 2600, it would do fine for the light antelope. The bane of the one gun hunter in Africa is rifle sighting. This of course becomes problematical with multiple loads however, the piece could be sighted in with one bullet, with adjustments noted on the scope bell for other weights. Or one could simply follow the advise of Kevin Robertson - "Load your .375 with 300 gr. Barnes X's and use it for everything."