This is the great controversy. I doubt it will ever be settled. The idea I have been insistently told. is to supply enough oxygen down to the breech area to hasten the burning up of glowing residue left in the breech. This precaution is taken to prevent a major explosion when the next powder charge is dropped into the breech. In quite a few
years spent at a busy range I never witnessed this happening. True, but it could happen they insist!
Most of us have owned a bicycle and put up with their habit of sneakily going flat in the tire area and we would fetch the old pump and slam in a number of pumps to bring the tires up to the desired hardness. Think about that. If you are a normal human being, the source of air with the least amount of oxygen in your immediate neighborhood is your lungs which have been grabbing it and using it to keep you ticking. This what you are using to make that unknown stuff burn to extinction. It might be better to force fully oxygenated air down your barrel with a quick wipe.
I witnessed an odd thing one day when a gent had a very tight fitting jag and patch get forced down a thoroughly plugged barrel. He actually was compressing the air in the barrel. He let go on the down stroke and the ramrod shot up and out of the barrel with enough force to hit the roof of the shelter.
Another reason given for blowing down the barrel is to clear the ignition channel. Usually the preceding firing of the gun has done that. In some percussion rifles, the hammer, when fired, will hold the expended cap tightly on the nipple and the back pressure of the explosion won’t open that nor will your breathing moist air down there.
The practice will continue, there is just no stopping it. In some of the cruder sections of Pennsylvania showing up with a lot of black powder residue is called Blowing the Coal Miner.