A rifle that is MOA at 1000 yards is WAY more than is needed for any game hunting, especially deer inside 400 yards.
Is there is difference between a $1000 rifle and a $4000 rifle? Yes, but there are few who can, or will, or even know how to take advantage of that difference. Most deer hunters pop a $100 scope on and have a combination of parallax and mechanical return (stock issues) inconsistencies that will keep those rigs at 1 MOA or worse even from a mechanical rest. A decent piece of glass and a solid stock added to most factory Remingtons, Weatherby's, Howas, Tikkas, Savages, Rugers will produce a sub MOA gun out to 400 yards. When you pass 400 yards, most factory rifles with the slower twists will start to leave 1 MOA and open up. Sure, there are now options of faster twist factory barrels and those can maintain 1 MOA further out. Long range matches have been won with $2K rigs and factory ammo over $10K rigs with carefully made handloads. There are many people who have a Remington 700 SPS AAC-SD with a $400 stock and $1000 glass getting 1/2 MOA out to at least 600 yards. It is probably the cheapest LR build you can get. If Remington would dump that crappy Hogue and put it in a stock with a mini-chassis, they would sell better to a small segment, but the $400 price increase would reduce their overall sales. So that $60 stock is actually a good deal for those who will dump it for a real stock.
The biggest difference between the $1k and the $4k rifle, besides the fact that they wear better glass, is in specific features. Usually bottom metal at $300 or so, some sort of chassis at $1K or so, scope rails with MOA built in and high grade mounts at $400 or so, and chambers cut with custom reamers to get the most out of heavier bullets, so $600 or so barrels. The most important part is the chassis system. With the ability to adjust the fit for different positions, it allows the shooter to be more consistent, keep the NPA the same, etc. and this results in better accuracy. IF you fired every round from a rack grade hunting rifle the exact same way with the exact same eye position and shooter to rifle interface, you would get a significant increase in accuracy.
Also realize that many of the best long range tactical shooters are running glass in the $3K to $10K range. They have more in their optic than I have in a whole rig. But I don't really want a 3 pound scope on a hunting rig either.
The average deer hunter probably has a 1 MOA capable barreled action. But they probably have 1-2 MOA added due to stock and optics and 3-4 MOA added due to their shooting technique. That leaves us at 5-7 MOA, which is what the average deer hunter prints at 100 yards.