The British might differ with your crediting Mr. Kimble, but I am not going to argue the point.
My point is that because the jug choke involves a longer opening, the bottle neck that is the " choke " part produces tighter patterns with black powder loads and velocities, with less constriction, than is required in modern shotgun barrels.
There are after market companies making long chokes for modern shotgun barrels using the same principles to obtain tighter patterns with modern guns. Some of the gun makers have played with the idea, too.
I know a good friend with a Remington 1100 barrel that has a long throat, which he used in shooting Registered Trap for a number of years. It also shoots slugs well, and with the newer Olympic shells, has produced some 98%, 40 yard patterns. ( 3 1/4 dram equ., 24 grams of No 7 shot, Gee Whizz velocity) The Barrel was given to him to try out by a Remington Executive at Vandalia, Ohio during one of the annual ATA Championship shoots there. It is not, nor has it been a production item.
A common practice among Trap Shooters is to relieve the throat of their modern gun barrels using a long tapered reamer. This tends to round the patterns, by getting rid of flyers, contributing to more pellets in the pattern,
too.In a slug barrel, it causes less damage to the sides of the slug as it leaves the casing, and improves the accuracy of shotgun slugs( the traditonal, Hollow base, Foster Style slug) remarkably. All of these techniques use the same idea: The longer the slope the less damage done to soft shot, or lead slugs, and the better the accuracy. The same idea is being jug chokes, and explains why they work so well. Today, long extension full choke, and " Extra Full choke" tubes are now being sold that deliver tight full choke patters at long range, for shooting turkeys, and crows. The long tubes have long shallow angle chokes in them, compared to the more abrupt chokes found in factory choked barrels, and choke tubes.