I have a bit of a problem with your conjecture that a 4" rifle is unsuitable for big game hunting, or that poor shooting is somehow mitigated with a more accurate rifle. If you can't shoot up to the accuracy potential of a 4" rifle, going afield with a MOA rifle has no advantage, you still won't be able to shoot within 4 minutes. But lets stop and think about what a 4 minute group, or 4" at 100 yards actually means. If your rifle is sighted so the center of your group coincides with your point of aim, no bullet strike will extend more than 2" from your point of aim. A tolerance of 2" on the center of a 12" target is meaningless.
The problem with the SKS is not the mechanical accuracy of the rifle, the problem is the hunter's ability to shoot up to that potential. Why? Because a very small stock, a short sighting plane, and a difficult trigger combine to make good marksmanship very challenging; mechanical accuracy and marksmanship are two different things. A light quick handling rifle, that fits the shooter, has a "glass rod" trigger and is equipped with a low power scope or a ghost ring and post iron sights, but will seldom puts 5 inside 4" at 100 is by contrast an excellent hunting rifle. A talented field marksman who can shoot up to his rifle, when shooting under good conditions, will never have a bullet land more than 2" from his point of aim. But all this is just a matter of probability.
If you put up a 100 yard target, and over sufficient time to prevent the barrel from over heating, you fired 20 shots, you would end up with a group that took on some interesting characteristics. The first thing that will catch your attention, is that no shot extends more than 2" from your point of aim, provided that your rifle is a true 4 minute rifle, and provided that you indeed are shooting up to it. The next thing you should notice is that the center is shot out of the target, and the group has not formed up in a ring 2" out from the point of aim. Rather some 80% of the rounds have impacted within 1" of center, thus the error potential is not 2", its more like half an inch. Thus we see that there is no reason why the cold bore shot out of a 4 minute rifle won't hit the point of aim 80% of the time. Any deviation from that is then a matter of of marksmanship.
We hunt in the real world. The climate in most parts of Canada from the end of August until late December can be challenging. Wind can buffet the hunter making a solid hold from unsupported positions impossible, and from high supported positions difficult. Fog, rain, sleet, and snow reduce visibility, and obscures the target. Cold temperatures numb fingers and rob the hunter of his feel for trigger contact and control. Heavy warm clothing screws up the rifle's fit, and the muscle memory developed throughout the long warm summer no longer works. This combined with the open ended timing when sighting on a live target, which requires the hunter to shoot before something changes, increases his sense of excitement, and decreases is marksmanship prowess. With all this in mind, the average hunter might as well be shooting a smooth bore slug gun as a match rifle, yet despite all that, somehow freezers get filled, and heads adorn walls.
