The military uses the .308 for long-range target threat acquisition and neutralization: Not the .22-250, and, in SOME special instances...the .223, or the .50 Barrett or the .416. But not always. Their first pick is the .308.
That should give you a clue.
Absolutely! The clue is the military uses what it has, and only goes to something "off standard" when the usual won't do well enough.
Every military uses its standard rifle round for everything possible. Always have. Since most have kept their .30cal-ish round for machineguns when they switched to lighter caliber general infantry rifles, tis still in the system, and still useful. The military uses the .308 because it works good enough, not because its the best possible choice for long range shooting.
I do love the .308 Winchester round, and while I don't compete, I'm very happy with it and have used it up to 600yds. Of the 3 choices, it is definitely superior in wind bucking, the heavier bullet simply drifts less.
The penalty for this performance is the size & cost of components, and the higher recoil. If neither of these is a concern, then absolutely the .308 is the way to go.