Exactly. I used to live in Alaska, and I’ve never heard of someone intentionally going after a Brownie with something as small as a .243.
I was station in AK the 1980’s twice and 30-06 with 220gn bullets were common for a bear gun. Heard a lot stories about guys on Kodiak using them with great success.
375HH were also popular.
The only person I knew who personally took a Grizz used a Savage 110 shooting 7mmMag.
Black Bears and Moose were taken with 30-30, 30-06 and even 12g.