Distinguished SOTW Member, Forum Contributor 2015-
Oxygen debt is not the issue.But then this leads to a curious situation that double-reed players have to deal with that single reeds don't. Because of the back pressure, you end up going into oxygen debt, and you have to expel the air that builds up along the way before you need to take another breath.
Bingo! The body's perceived need to breathe is triggered by the buildup of carbon dioxide - NOT the lack of oxygen.Oboe uses notoriously little air, and oboe players sometimes have to actually expel breath and then breathe again to keep playing when the carbon dioxide content builds up too much in their lungs. Bassoon uses much less air than sax for the same note.
A tenor sax easily flows more air than a bassoon. So does my soprano setup. Just look at the throat of a bassoon reed and a bocal - much smaller inner diameter. And then there is the matter of the geometry inside a bassoon reed...