She's also the one that brings Pit back to live when he's finished.
She also takes the role of mission control since she's the one that knows the other gods, enemies, locations and what's going on.

So she's kinda the King in a chest game, not a good fighter, but she's the one with a plan and the game's over if we lose her.

Kinda, sorta. It's weird.
In the original NES, it is all about Pit going up against Medusa and her army while Palutena is basically trapped.
But, in the NES game there's parts where Pit could somehow fly. When it's a plot point that he can't. Kinda implying that it was at this point Palutena gave him the power to fly.

And in Uprising, Pit needed Viridi's help to save Palutena.

So, to put it simply, Pit needs Palutena or another god to get things done.

And I understand that Palutena can be mean to Pit. But it's not like she doesn't care for him.
After the NES game, she promoted him from grunt to her right hand man. And in Uprising, after Pit burns his wings, the first thing she did was figure out a way to fix him up.
So she does care, she just like teasing him.