Seems to me that blowing down the barrel to extinguish a smoldering patch is a strange decision since oxygen is usually introduced to make smoldering items catch fire.
Sticks. Leaves. Campfires. Charcoal. Foundries. Etc.
Cut a two small pieces of char cloth, both the same size, say a half inch square. Touch a hot wire to the edge of each. Both will now glow and smolder. Now time how long it takes to go out having burned up the char. One is just glowing while you blow forcefully on the other. One will glow for several seconds the other puffs all out quickly
Blowing on an ember can blow it to flame but also quickly extinguishes it.
Blowing opens the touch hole proving there is nothing to block the flame from the prime, this works also on cap guns
Blowing humidifies the fouling and keeps it soft, these are the reasons to blow down a barrel, but if there is an ember, keep in mind how small such an ember would be, it quickly blows it to life using up all the available fuel in a quick burst of air.
Not doing it is a matter of appearance not safety.