"Not For Ball' & etc originated from the fact many shotguns, from muzzleloader days into early breech-loaders were habitually used with round balls for larger game. It had been common practice to use a close-fitting ball to the bore of the gun for better accuracy. With the common acceptance of choke boring in the breech-loaders, a ball sized closely to the bore would obviously play havoc with the choke.
By at least 1910 W W Greener wrote that even guns marked Not for Ball could be safely & effectively fired with a solid ball "Provided" a small enough ball was used to pass through the choke. Thus if a nominal 0.729 12 gauge was given a full choke down to about 0.690" choke then the ball had to be smaller than 0.690" in diameter. A commonly used 0.719" ball would wreck the muzzle end of the barrel.
He further stated this was the reason the British proof houses changed their markings from "Not for Ball" to the simple word "Choke".
That's been at least 110 years ago, Weird that so many folks Still Haven't Caught On.