Gas exchange also doesn’t happen in your arteries or veins, but in your capillaries. Your capillaries are small enough to just barely fit a single red blood cell (the RBC often need to bend to fit through) and that close contact of RBC and capillary wall allows fast and near complete gas exchange. The tightness of a capillary is a feature, not a bug. So it could be that you don’t have consistent contact with the same RBC for long, and mostly are in contact with blood plasma?

Ah, so more or less the opposite of my guess. Man, I love Cunningham's Law!