If you did much hunting at all before the invention of laser rangefinders and MOA reticles, it would be easy to understand the popularity of the 25-06. Fast flat shooting cartridges were popular, because accurately judging distance was extremely difficult, and almost everyone was doing holdovers with a regular crosshair.
The 25-06, though not as efficient, is still a nice step up from a 243, especially in the days before "ballistic apps". It hits harder, shoots flatter and helped people be more successful in the field. With 75 Gr. bullets it can do 3800 FPS and is an creditably flat shooting varmint round.
I have seen more deer killed with 243's and 25-06's than anything else and, to me, it seemed the 25-06 almost always performed better.
There are even a couple 25 cal. bullets that are almost legendary - the Sierra 117 Gr. Pro Hunter, and the Nosler 120 Gr. partition
Given all that, when my 25-06 wears out, I will re-barrel to a 6.5 something...