The OP is describing medium bore rifles. Yes, there is absolutely a place for 375HH/9.3x74R class doubles. Especially so for Alaskans and Europeans that might use them in the timber for running boar, bear protection, elk, woodland bison, etc, etc.
What about smallbore double rifles? 7x57r, 7x65r, .303 British? Yes, there's definitely a place for those as well. They are wonderful for getting off a very quick follow up shot on elusive creatures at close range.
If I was going to own a double rifle "for all seasons" in addition to specialty magazine rifles, I'd own a 375 Flanged. It is wonderful for deer, boar, and larger North American game. It's wonderful for all the African plains game, inclusive of Giraffe and Eland, and its functional for leopard, lion, hippo (brain), and buffalo.
Basically, it can do everything marginally or adequately except for body shots on Hippo, Elephant, and Rhino.
That's a pretty good compromise double rifle.