The average speed of a cheetah is 40 mph. And so is the average speed of a racehorse. They both run with their mouths closed.
Nose breathing is efficient. You get 20% more oxygen delivered to your organs, muscles, and tissues.
Efficient breathing puts less effort on the body. You’re conserving energy, allowing you to do your activity better/faster/longer.
On the flip side, the effects of improper breathing need to be compensated by other parts of the body. If you breathe too fast, your heart beats too fast. You get tired quickly.
You can rely on your nose during physical activity more than you think you can. You only need to start small and work your way up. Next time you’re exercising, try to close your mouth and breathe through your nose only. You might need to slow down a little, but soon you’ll be able to pick up the pace and feel less tired afterward.
I know this through personal experience. I used to run out of air going up the slightest hill — gasp for air, breathe fast, and feel lightheaded and tired. Since I've been conscious about my breathing during exercise my endurance has improved tremendously. I don't dread going uphill anymore. I don't feel my heart pounding during hikes. And I enjoy the activity!
Stay healthy, stay happy.