I agree with Gene that a hunter needs to be able to hit close to his point of aim, at whatever range he's hunting. Given a reasonably accurate rifle & load, the prime limitation is shooter skill.
We often talk group size, and that's fine, but more important to me is if I can make the hit, with the first shot, in the field or at the range.
Try that rifle of yours out at 300 - 600 yards to see how the groups hold up. Often groups open up considerably at longer ranges, when they were solidly sub MOA at 100 yards.
I've got rifles I'm perfectly happy with, for their role, that really don't group very well. Am not looking to do any long range/precision shooting with my .30-30 Marlin or my .50 cal traditional muzzle loader for instance. Have an old beat-up .30-06 that continues to deliver the goods although it's well past the point where it could use a new barrel. It's good for 300 yards, but I wouldn't ask much more than that of it. At 100 yards, it can still produce roughly MOA accuracy.
The two rifles that I do consider my long-range hunting rifles can shoot 1/2 MOA out at 300 & 600 yards, when I'm doing a decent job of reading the wind and making good shots. I feel confident in the rifles, loads, and scopes - and I realize that with those rifles, I'm very much the weak link in the equation.
FWIW, Guy