Smallfry: I have three close friends who Hunt all manner of game with the 25/06 Remington caliber, INCLUDING Elk!
I have pair of VERY accurate 25/06 bolt action Rifles myself.
I don't Hunt Elk with them but I have seen two of my friends kill Bull Elk with their 25/06's.
I have seen one of my friends kill both Mt. Goat and a Black Bear with his 25/06.
Bullet placement and quality construction are most likely keys with this caliber for the larger game.
I have killed three kinds of Deer, Antelope, Coyotes and Rock Chucks with my 25/06's and have had it along on several Wolf Hunts (no luck there as yet).
I always have made it a point (for the last 50+ years anyway) to casually inquire of Hunters I come across afield (both Big Game Hunting and Varmint Hunting) which caliber Rifle they are using.
The 25/06 is and has been pretty popular here in the west.
The 25/06 Remington does a LOT of things very well indeed!
Long live the 25/06 Remington.
Hold into the wind
VarmintGuy