In some processes it definitely makes a big difference to add other gasses without removing the oxygen (that is, to increase the total pressure too). Where diffusion is involved, having another species in the way slows things way down. And even when there’s advection, the last teeny bit of the way is just diffusion.
The working fluid in a heat pipe is very much inhibited by the addition of a bit of other gas. I think heat transfer coefficients can be on the order of 10^5 at the interface if the working fluid is pure but can drop by orders of magnitude due to a minor share of something else (at least that’s the number I think I remember for this parameter).
If the oxygen is interacting at a surface in some way that consumes it, with no other gas present there can be a bulk flow toward the surface (and in the heat pipe example one of the flux limits derives from the local speed of sound for the gas phase in bulk flow). If there’s another constituent present, it piles up at the surface and creates a concentration gradient for the oxygen to fight through.
I don’t know if it’s a problem in health particularly, but generally speaking, there are ways adding even a small amount of something else greatly reduces gas availability and reaction rate.