I think you may have defined it: 300 yards. An average diligent shooter with an adequate cartridge can hit the vitals 80% of the time at 300 yards. Several cartridges are adequate -- .30-06, .25-06, .270, .338. Wind effects may not normally be significant at 300 yards. Some negotiation may be necessary to agree on the definition of "average diligent shooter." For me, an average diligent shooter practices shooting several times a year which may include shooting from the bench, shooting from field positions, dry firing from field positions (I do a lot of this, personally, and find that it is a valuable contributor to steadiness -- I'm not sure how many other people do or who may also agree with the value of this exercise). The average diligent shooter confirms his rifles zero immediately before a hunt -- within a week of the hunt or less. The zero should be appropriate, for example 200 yards or 225 yards. The average diligent shooter has selected a load which shoots decent groups, for example 1.5" or better, and uses the load with which he has zeroed his rifle on the hunt.
At 400 yards, maybe the .30-06, .270, .25-06, .338 aren't your best choice, as they are dropping quickly at 400 yards. Then you may need to think about a more specialized cartridge. When you get beyond the point-blank range of the cartridge, where the bullet is dropping fast, the shooting becomes much more difficult because your range guesstimate must be very accurate. Wind effects become significant and you probably need to be able to dope the wind proficiently to achieve the 80% vitals hit. Wind effect is not linear with range. And, of course, at 400 yards the human error is just that much more opening up of your group. It becomes a whole higher level of difficulty, in my opinion, to hit in the vitals 80% of the time at 400 yards.
I feel comfortable shooting at 200 yards. I think 300 yards is getting to my limit. I have shot a pronghorn antelope at 240 yards, and while I felt comfortable with the shot, I was "feeling the range." I think I can see whether I am within my range limits or not. That is, how steady I can hold is something I can see in my scope. My range limit is not so great that rapid bullet drop or wind drift become effects I have to compensate for. I have to worry principally about my ability to hold steadily on target, and this I can observe in my scope.