Guy,
I've owned and hunted with a number of No. 1's, from .22 Hornet to .450/.400, and agree completely, especially in North America. Actually, my favorite No. 1 for general big game hunting right now is a .25-06, a 1AB special-run from Lipseys with fancy European walnut. I'd certainly hunt anything in Montana with it, unless we get a grizzly season again.
That said, it's still hard to beat a .375 No. 1 as an all-around rifle. I've asked a number of the African PH's I know whether they would guide somebody who wanted to use a single-shot on Cape buffalo, and I can't recall one who said no. In fact most said something like, "Why not? It's the client's hunt, and the first shot is by far the most important."