In fact multiple species of oxygen or nitrogen can create emissions at various wavelengths. There can be aurorae over a wide range of wavelengths, we just see only some of them that happen to be in the visible range. So, it's all a matter of which species hit the relatively narrow visible target.
With respect to oxygen, Rezaei et al. 1 provide this spectrum, in which atomic oxygen produces an emission near the red end of the visible range, while ions of both monatomic and diatomic oxygen give less intense emissions of various colors from blue to orange. Note that no emission is listed for neutral $\text{O}_2$.
With nitrogen, similar results from Hosseini et al. 2 show an emission in the violet or blue range from ionized diatomic nitrogen, but none from any monatomuc nitrogen species. Note that in this spectrum the red eemission from atomic oxygen is seen, apparently from a small amount of this imputity in the gas sample.
References
1.
Rezaei, Fatemeh & Abbasi-Firouzjah, Marzieh & Shokri, Babak (2014). "Investigation of antibacterial and wettability behaviours of plasma-modified PMMA films for application in ophthalmology", Journal of Physics D Applied Physics, 47, 085401. https://doi.org/10.1088/0022-3727/47/8/085401.
2.
Hosseini, Seyed Iman & Mohsenimehr, Soad & Hadian, Javad & Ghorbanpour, Mansour & Shokri, Babak (2018). "Physico-chemical induced modification of seed germination and early development in artichoke ( Cynara scolymus L.) using low energy plasma technology", Physics of Plasmas, 25, 013525. https://doi.org/10.1063/1.5016037.