If "large game" is basically elk, lots of non-magnum cartridges are just fine. Same for moose, although there's a lot less moose hunting than deer or elk. If the Alaskan bears are on the agenda, a separate rifle for them in some magnum caliber is a wise choice.
Staying with deer for a moment, as far as I'm concerned, anything from .243 to .30-;06 works just fine. Old age has taken me out of the walking-hunter category, so I've quit the '06 and gone to a 7mm08.
Elk? Generally, anything in the .270 to '06 class of non-magnum works. Few use the .243, but quite a few like the 6.5 class of cartridge.
Magnums give more range, but that's needed in more specialized hunting. The longer distances of shots in the more open country of the western states is an arena which can justify the added recoil. Or, the long distances of "beanfield" shooting in farming country. Again, less common for most hunters.