Why would this reaction occur? Won't it be unfavourable?
You're right: $\ce{NO}$ is a free radical and the reaction between $\ce{N2}$ and $\ce{O2}$ can be achieved - supposed that enough energy is provided.

This may happen through an electrical arc discharge in the lab or, in the mesosphere (50-85km above earth) through ionizing cosmic rays. Note however that nitric oxide react with oxygen to eventually furnish nitrogen dioxide $\ce{2 NO + O2 &lt;=&gt; 2 NO2}$.