Depends on the rifle.
A 30-06 covers every base pretty well in the USA. It is probably maxing out it's abilities for buffalo and it's awful big for ground squirrels, but in skilled hands with good loads designed for the game, it will do everything.
The 308 will match it with 150 and 165 grain bullets, but bullets over 165 grains give up a bit to the 30-06, and in some guns because of the magazine length, you can't use the very long bullets over 200 grains very well.
So to me I would ignore the abilities of the cartridges if (A) you were never going to hunt bison with it and (B) you don't intend to shoot many ground squirrels.
So my answer is yes, I would buy a new rifle, but I would probably not care about the cartridge as much as I would the rifle itself. As an example I might fall in love with an M-1 Garand. Or I may come across a nice custom made Ruger #1 that I just can't live without. If it was a 30-06, or a 308, or a 270 or a 338, it would probably not effect my buying the RIFLE if I just liked it.
I might be more caring about the cambering of such rifles if I were in the sad place of not having any, or very many rifles already. For a one gun hunter I still recommend a 30-06, but it has very little advantage over the 308 or 280 or 270 in the real world.
We love to talk about the "one rifle for all game" but if we are honest, we have to admit that if someone can afford to hunt white tails, fox, prairie dogs, elk, moose, mule deer, caribou, coyotes and bison it's probably certain he can afford to buy a few rifles to do it with.
