A few counter anecdotes: I read a story about a baseball coach making the players hold water in their mouths while training to make sure they couldn't mouth breathe. I'm pretty sure if you watch an MMA fight the fighters will mostly have their mouths closed. And the airway-focused orthodontist Bill Hang ran a marathon with tape over his mouth (only removing it for hydration) to make a point about the importance of nasal breathing. Also, I can do sustained moderate to high intensity exercise with only nose breathing.