Funny how many people here have openly mentioned the risk of flying snot, yet in martial arts circles it is the thing that is rarely spoken about (despite the fact that it happens).
Also, back on topic, my understanding is that the desired amount of tension in the posterior chain and core (for desired expression of power) just cannot be generated as efficiently by breathing out through the nose vs. the mouth in the time allotted to discharge air on the exhale. From my own observation there is more tension generated as I breathe out through the mouth vs. the nose, and IMO it is because of how fast the air is discharged from the lungs (greater volume discharged through mouth vs. nose in the same amount of time) -or- stated differently, same volume discharged at a faster rate through the mouth.
Remember that power is a metric that measures a
rate of force expression, which in simple terms means a force expressed (or more appropriately, work done)
over time. Even if maximal force is expressed, you are not maximizing power unless you minimize the time over which that work is done, hence wanting to generate that appropriate tension in the shortest possible amount of time.
Just my $0.02, YMMV
Edited to add:
@WxHerk that largemouth in your avatar is awesome!