Fired my .375 H&H, with 270 grain bullets, for the first time in a long time last week. It is true, recoil may affect accuracy. My shoulder has fully recovered now thank you. Bigger is not always better.

Colorado perspective here and that is important. There are several big game loads that are more versatile than others. I may suggest the 30-06, 7MM Mag, and .300 Mag as being usable for a fair number of large game. The .308 and .270, and others, also hold their own in terms of versatility.

Bears?
Black bears: ~.30 caliber rifle
Grizzly and Alaskan Brown bears: .375 H&H
Polar Bears: Are you out of your mind?