Throughout the story, we see that Katniss was never a fan of the Capitol lifestyle, the crowded places, the people, politics and anything involving the government.
As soon as she saw that the 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.
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.
Taken from the book:
We learn to keep busy again. Peeta bakes. I hunt. Haymitch drinks until the liquor runs out, and then raises
geese until the next train arrives. Fortunately, the geese can take pretty good care of themselves. We're not
alone.A few hundred others return because, whatever has happened, this is our home.
Peeta and I grow back together. There are still moments when he clutches the back of a chair and hangs
on until the flashbacks are over. I wake screaming from nightmares of mutts and lost children.