There's a difference between oral/ nasal, chest/diaphragm or stomach breathing. You can breathe into your stomach using your mouth or nose, no need to engage the the upper body with either.Nasal, diaphragm breathing is superior to mouth breathing for a number of reasons. It has nothing to do with oxygen intake, but muscle needs.
Easy test, take a deep breath with just your nose. You just used only your nose with a little help from your diaphragm, the most important breathing muscle of all, and all that air bypassed your lips, teeth, uvula, and esophagus, straight down below.
Now, take a big lungful of air with your mouth. Your whole upper body just engaged. Multiply both by 100 breaths (a few minutes for some, half an hour for others). So much wasted energy. Great if you need to gasp.
Is It Better to Breathe Through Your Mouth or Nose During Exercise?
Should you breathe through your mouth or nose when exercising? It turns out nasal breathing running—not mouth breathing—may be better.www.triathlete.com
The article looks to be a classic case of scientific misrepresentation. The study says nasal breathing doesn't impact performance in running, not that it improves performance. If you take the rest of the article's info you could make that argument on the bronchial constriction argument, but if you're not running in cold dry environments it's a non issue.
Half baked articles backed by science are a pet peeve of mine. They often skim the abstract and don't really understand it. With the importance of grabbing attention these days, many study authors over sensationalise with titles and interviews to the media too.
I'd be interested to see a study on recovery rates based on different breathing modalities. No impediment to activity at steady state or anaerobic levels (which doesn't use oxygen in energy production) is one thing, recovering after anaerobic activity is another. There probably are studies, but I've got other things to do than track them down right now!