coach the new tribute.
Exploring the series from that perspective would have been interesting (though she somewhat did it in Songbirds and Snakes).
Have Katniss fail and watch her tribute die which encourages her to spark the rebellion in Book 3 would have been a more interesting plotline to me than:
HEY! IT'S AN ANNIVERSARY AND YOU CAN DO IT AGAIN! and Book 3: IT'S THE SAME THING BUT IT'S IN THE STREETS!
Lots of potential after the first book (and I did enjoy reading books 2 and 3), but ultimately fell short of what it could have been, IMO.