Actually, I think "Pegasus" drives home just how much the fleet needs its civilian government, and what it would be like without it.
The Battlestar Pegasus is the exact path Adama almost went down, if not for Roslin convincing him that the war was over. Back in the miniseries Adama wanted to go back and keep fighting the war. Pegasus has got "tunnel vision" as its been described, it is locked only on the idea of destroying the Cylons, not perpetuating the human race, not finding a new home. Cain is still trying to "win" the war, with one ship against an entire race, and odds like that only work in video games.
If it hadn't found Galactica, the Pegasus would have eventually been destroyed by the Cylons (or their self-destructive behavior), it would slowly be run out of personell, vipers, armaments, and eventually worn down. The Civilian government and presence with Galactica is what keeps them realizing what they are fighting for, and why they are fighting.
The Pegasus is locked in a vengeance mindset, still fighting a war they lost months before, because all they had to live for is fighting. The civilian government reminds the Galactica that their first priority is to the survival of the human race, not pursing a lost war. Without a civilian government, we saw what happened to Galactica, and how very quickly it turned bloody and everything fell apart.
If not for the Civilian government, Galactica would still be fighting to the death back in the colonies and they would never have unlocked Athena's Tomb and found the path to Earth. Without the Civilian government, the human race would have died out to the Cylons.