I don’t know that. Any data or link to a study that support your claim, this more efficient oxygen use through nasal than mouth?
From my understanding of high altitude breathing, people that live in high altitude have either higher density of hemoglobin in their blood as the case of the study on people who live in Andes, "Andeans counter having less oxygen in every breath by having higher hemoglobin concentrations in their blood," as quoted from the article below
https://www.google.com/amp/s/relay....e/2004/02/high-altitude-adaptations-evolution
Or breathe faster, as the case of people who live in Tibet. “Tibetans compensate for low oxygen content much differently. They increase their oxygen intake by taking more breaths per minute than people who live at sea level.”
When I hiked up Kilimanjaro (19,341 feet) I did experience with increase breathing rate. However after 3-4 days high altitude acclimation at around 13,000 to 15,000 feet, before summiting, my breathing rate calmed down to normal level. I was told that my body was adjusting to the low oxygen environment by producing more hemoglobins in the blood.