Might have been something to that 'striking for balance' notion back before the invention of the lathe.

As Miller knows, taking any significant amount of metal off a barrel would be a lot easier in a machine. And you can also file in a lathe a lot faster than on a barrel stuck in a vise.
Any of you that have measured wallthickness have seen that barrels, for the most part, have a constant wall thickness from muzzle to about 15" +/- from the breach. Then many have two straigth tapers, one shallower angle from the thin section, and another steeper angle to the breach. These angled tapers are blended enough in the "striking" process that they are often not noticed and thought to be a smooth single taper or even a radius. Holding a set of early 20th century barrels up to a light source and looking down the outside makes the two tapers evident. If I were to guess what purpose of "striking" was, I would venture to say it was to blend these three cuts and remove the machining marks.
Any manufacturer that has ever tried to machine and finish a product of any kind will always strive to maximize the use of the machine and minimize any hand work. This is as true today as it was in 1900. Anyone that doubts this, I recommend you go buy a 30" bar of 3/4" diameter mild steel, which should cost about the price of a meal at McDonalds, and try to hand file .010" off the diameter the full length. I'll check back with you in August. Oh, and keep it round too.