Aurora borealis - less favored energy transitions higher in atmosphere?
Why don't you see a mix of the two colours? After all, from the collision rate argument you would expect fast transitions (like the green of atomic oxygen) to become even more prominent. 


There can be a mix of colors.  However, according to Auroral electron energy derived from ratio of spectroscopic emissions Journal of Geophysical Research Volume 79, Pages 5181–5186, the ratio of the atomic oxygen versus molecular nitrogen bands are a function of "a characteristic energy of the precipitating electron flux".


  Why is it that some transitions are less likely as you increase in height?


Well, consider Atmospheric Composition and Vertical Structure.  Figure 3 shows how dramatically pressure drops as altitude increases.  This means a change in altitude of 15 kilometers could reduce the concentration of the species of interest by a factor of 10.  

In addition, dissociation of the $\ce{O2}$ and $\ce{N2}$ to atomic O and N increases with altitude.  See especially Fig. 6 which plots the points where monoatomic oxygen starts to exceed diatomic oxygen, and where monoatomic oxygen starts to exceed diatomic nitrogen in concentration.