Throughout the story, we see that Katniss was never a fan of the capitol life style, the crowded places, the people, politics and anything involving the government.
I think all she really wanted is to go back home and start a new simple life as she did. Have a farm, a family, away from the troubles.
As soon as she saw that capitol would be in great hands with the new president Commander Paylor, she saw that she didn't need to be involved in any of that.