This idea might be completely bonkers. Infact, I am pretty sure it is complete bonkers.

You know how you can make the AI run every faction and turns becoming automated by cheats? Now get this; what about that as a simple click in the new game menu, and you get to choose to see or skip the battles that occur!

This might even be possible as a mod. Either way, I think it would be fun because sometimes I just want to see impressive space battles without the need to play for hours before getting there.