A bullet pattern is a cone...the further out you go the wider the cone and vice versa.
We aren't talking about shooter error here, we are talking the "mechanics" of the gun. 1.5" @ 50 yards equals 3" @ 100 yards. If the kill zone is 6" then a sighted in rifle at 100 yards is going to hit in the kill zone.
That said, the biggest factor in accuracy is the "trigger actuator". Some people can't hit their butt with both hands, let alone a paper plate at 100 yards, so the most accurate gun in the world won't help.
It all comes down to knowing your guns limitations and your limitations. A 2" group at 50 yards is more than adequate for hunting at 100 yards IF YOU CAN DO YOUR PART AND YOUR GUN IS SIGHTED IN AT 100 YARDS.
If it is sighted in at 50 yards, you will be low at 100 yards and some shots will be out of the kill zone given your gun will have 4" spread at 100 yards and the associated drop.
So it all depends on the person shooting, the "point blank range" you are using and the accuracy of your load.
Me: 2" group or less, sight in at 50 yards with a "point blank range" of 100 yards and I am good to 120 yards if I do my part.
There is wisdom in the paper plate system, if and only if, you are using it to determine your max distance to shoot using the shooting position you would use in the field. If you can put all of your shots in the 6" plate you are good AT THAT RANGE. Keep moving it out until you can't....I am talking about NO BENCH REST shooting, rather standing or sitting, what you would use in the field. When you can't keep them in the plate, then that is your max range.
Point Blank Range:
https://en.wikipedia.org/wiki/Point-blank_range