One of Litz's book covers the OP's topic pretty hard. He has a program that's called WEZ (weapon employment zone), you can plug in a slew of variables (rifle precision, range, target size, wind calling ability/variability) and it'll punch out a number giving you your statistical likelihood of connecting. The long and the short is that unless you are shooting at very small targets a ways out (which are already statistically low probability shots to begin with) that you hit the point of diminishing returns (in terms of rifle precision) pretty hard at 1 moa. There's obviously no downside to a more precise rifle but it doesn't get you much more in terms of hit probability.
Now in terms of field accuracy, it mostly comes down to having a very good understanding of your accuracy capability with the particular system that you're using in the particular positions/situations that you're most likely to use where you're hunting. You can easily practice for this at the range by shooting paper at 100 yds. A buddy of mine came up with the Kraft drill (it's pretty well known in PRS/practical precision rifle circles) where you essentially shoot 3 rounds in each position (standing, kneeling, seated, prone) at a diamond target with concentric diamonds going from 1-6 moa or so. It's since been refined to 4 different diamonds, one for each position. Regardless, you can do it on any target. The point is, you get a very good idea (if you shoot the drill often) of what your accuracy capability is in each of those positions. Whether you do it supported positional, unsupported, off a tripod, whatever doesn't really matter, it just allows you to know how accurate you are with your rifle in that position. When you combine whatever that group size is with the knowledge of how much your bullet will be moved per mph of wind at each range and how well you can call the wind on average (2mph, 3mph, 5mph?) you can start making really educated decisions on what is or is not, an ethical shot. Obviously other factors come into play as well such as backdrop and terrain (if the deer runs, will I be able to see where?) but from the standpoint of knowing your capabilities, positional shooting at paper targets at 100 can pay huge dividends.