Six in one hand, half a dozen in the other.
Yes they are great ballistacally and served well in both wars..
Well what more do you want?
The military switches to other cartridges usually to allow the soldier to carry more ammunition that what they use to carry.
Aside from all the political BS. A soldier can carry quite a bit more 308 rounds than they could a 30-06 and since most combat was fought at relatively close distances the extra power of the 30-06 simply wasn't needed in military applications. The 308 recoil is also lighter so a soldier can sustain accurate fire beter than he could with the 30-06.
You also have the advent of better powders, better bullets, etc... that make the modern 308 better than the 30-06 before these improvements in propellants
Basically what the military desides in the way of what cartridge they are going to usehas about zero correlationto what is useful in the hunting world. Take the 5.56 as an example. They switched form the .308 to the 5.56. Does that make the 5.56 a better big game round???????? Of course not.