I use a 6.5 G for exactly that. NF 2.5-10 scope allows you to take advantage of the cartridge better than the aimpoint, since the 6.5 works great from 0-800 yards or more.
6.8 with an aimpoint would be a great 300 yard and in big game/GP rifle.
5.56 is still hard to beat for everything but big game hunting. I'd take it after deer or pronghorn, but nothing bigger. I also like that I can burn a 1000 rds through it in a weekend like nothing, and all that training translates to the 6.5 nicely.
If 6.5 G and 5.56 cost the same, I would have my one rifle I've been searching for all these years. Alas, the search continues.
While I understand this, it boiled down to a few key facts for me.
1. My carbine is going to be most likely used to save my life within about 25 yards.
2. My carbine's most valuable potential use is to save my life or that of a loved one.
That said, I picked the best optic for me, for 0-25 yards. That turned out to be an Aimpoint (If you like Eotech, that's great, too, lets not go there...), as I just don't think a 1-X variable can compete with Aimpoint's brightness, durability, and 1X use up close, especially in awkward or less than ideal presentations.
Then I said...
What do I enjoy doing with my rifle?
Well, I enjoy shooting things with it. Near and far. I want to hunt with it. I like punching paper. I enjoy all sorts of things. So I added a magnifier which allows me to see my hits at 100 yards, which allows me to place bullets precisely on vermin, etc.
Basically I set my rifle up for what it is most likely to be used for. Not the 0.001% chance of what it might be used for.
YMMV