Nah. Big is way overrated.
We do of course have the shining example of the Canadian Rangers. Well worth looking them up, interesting history and stories.
From 1947 until 2015, yes 2015, the Rangers were issued - wait for it - the Lee Enfield No.4, in .303 British. Hard case, eh? That was specifically for protecting themselves against bears.
In 2015, they were of course issued with a slightly upgraded new rifle, the Tikka T3 Compact Tactical Rifle in its “Arctic” guise, made under licence by Colt as the C19, and chambered in .308 Win.
Not a .375 or a .45-70 or a whatever. A .308. Because, you see, the Rangers have titanium bollocks. And they know their way round a charging bear. Power does not automatically equate to success, being very, very cool when it counts does. Same for shooting anything big and hungry.
(I’ll add that actually, delivery of the new rifles only started in 2018-19! And I want one.)