Isso é um choque; um que precisa ser resolvido em algum tipo de clímax.

Boggs, o motivador
Boggs faz duas coisas extremamente importantes:

1. Faz com que Katniss perceba que ela mesma é uma peça importante neste jogo
2. Define Katniss como líder do esquadrão 451, confirmando que ela deve seguir em frente com sua missão (Kill Snow)

De Mockingjay :

"Sometime in the near future, this war will be resolved. A new leader will be chosen," says Boggs.
I roll my eyes. "Boggs, no one thinks I'm going to be the leader."
"No. They don't," he agrees. "But you'll throw support to someone. Would it be President Coin? Or someone else?"
"I don't know. I've never thought about it," I say.
"If your immediate answer isn't Coin, then you're a threat. You're the face of the rebellion. You may have more influence than any other single person," says Boggs. "Outwardly, the most you've ever done is tolerated her."
"So she'll kill me to shut me up." The minute I say the words, I know they're true.
^{-Suzanne Collins, The Hunger Games: Part Three 3 - Mockingjay, Chapter Nineteen. [emphasis mine]}

e quando ele

dies

ele dá o "Holo" para Katniss, fazendo com que ela se mova ainda mais com sua "missão":

"No. Boggs gave it to me," I say.
"Don't be ridiculous," she snaps. Of course, she thinks it's hers. She's second in command.
"It's true," says Homes. "He transferred the prime security clearance to her while he was dying. I saw it."
"Why would he do that?" demands Jackson.
Why indeed? My head's reeling from the ghastly events of the last five minutes--Boggs mutilated, dying, dead, Peeta's homicidal rage, Mitchell bloody and netted and swallowed by that foul black wave. I turn to Boggs, very badly needing him alive. Suddenly sure that he, and maybe he alone, is completely on my side. I think of his last orders....
"Don't trust them. Don't go back. Kill Peeta. Do what you came to do."
What did he mean? Don't trust who? The rebels? Coin? The people looking at me right now? I won't go back, but he must know I can't just fire a bullet through Peeta's head. Can I? Should I? Did Boggs guess that what I really came to do is desert and kill Snow on my own?
^{-Suzanne Collins, The Hunger Games: Part Three 3 - Mockingjay, Chapter Nineteen. [emphasis mine]}

Vendo que foi

a Rebel plan to set-off the double-exploding bombs (killing Prim), and not President Snow's idea ^[1]

permite que Katniss perceba que

Coin is really just another substitute for Snow. Worse in fact that she will do whatever it takes, including kill children (including Prim) on public television to get her way^[2]. Ultimately leading Katniss to Kill Coin instead of Snow!

Este é o enredo mais importante que ela ganhou em sua missão no Capitólio!

Peeta
Katniss vê e descobre que durante todo o tumulto do esquadrão 451 tavels, Peeta não a mata! Ele é capaz de mudar e ser mudado. Se ela não tivesse visto isso por si mesma, ela pode não ter sido tão aberta a ele

returning to District 12 and living with her.

Ela vê que através de múltiplas ocasiões e oportunidades para Peeta matá-la, ele não o faz . Ela aprende a tratá-lo com um pequeno grau de confiança e uma enorme quantidade de humanidade.

TL; DR: Continuar no Capitólio foi útil porque:

1. what happens there helps Katniss realize Coin is not to be trusted.

e

2. Katniss was able to observe Peeta's recovery and begin to trust him again.

^{[ Nota: Ainda não vi o filme, pelo que a minha resposta será apenas baseada em livros; Eu confirmarei / repreenderei minhas descobertas uma vez que vi o filme Eu assisti ao filme, e confirmei que os eventos foram quase idênticos ao livro.]}