Likely back in the day it was mostly trappers checking lines that encountered the odd Grizz and used the 25-20's 30-30's etc, not actively going out after Grizz with those cartridges.
However there was a much more aggressive predator extermination plan in the US turn of the century, and they probably used more adequate cartridges for the specific tasks.
Back in the day there were few elk or moose, guys around here hunted deer, sheep, and goats. 25-20, 32-20, and 44-40 were the cheapest centerfire cartridges. The rifles were more affordable and they packed well on horses, as well as being quieter and didn't disturb the whole country side, don't forget, a Winchester was also a status symbol. Grizzlies were shot on sight. The ones that caused trouble were the old boars that don't hibernate, trappers would spend all day on snowshoes and so would pack a light 22 which they would use to shot goats for meat. And of course a 22 is woeful for use on Griz.
I'm looking at a catalog from 1961, which post dates what I posted, you could buy a 338 WM for $165, but there is no ammunition listed.
Speaking of ammunition, I have a hunch that there weren't very many 45-70's in Canada, Dominion did not seem to load for it whereas they loaded for the 43 Mauser.