This seems fairly straightforward. In a nebula, I feel like my champion has very little actual impact. Dont get me wrong, that isnt to say he is completely useless (I'm pretty sure most of the nebula missions if left alone would result in a loss), but sometimes I just dont feel like he does anything important.
In the majority of them, I do a lot of waiting around until my allied heavy units decide to actually do something useful (read: assault a base). At which point I support them by shielding them with the projected shields. And thats about it. I can sit there for a few minutes doing that, and then either the base is dead or I am out of energy. What use are my main guns? I dunno. Dont seem to be very useful. My modules I mean seem kinda important? Not really?
I honestly feel mostly constrained by "does the ai want to use its heavy ships to kill something yet". If that magically is yes, stuff happens. Otherwise..... *shrug*
Outside of nebulas, my champion is basically the strongest single ship in the galaxy. Inside of nebulas, I feel like it is only useful for the shields.