Why have Kira, Thomas and Jo been taken to the Edifice in Gathering Blue?
Kira, Thomas and Jo are possessed of an almost magical talent that gives them the ability to, respectively, weave incredibly intricate scenes with beautiful colours, carve amazingly detailed depictions into wood and lastly, sing incredible songs. They have the ability, through their talent, to predict the future and what will happen to the world. Kira's job, after all, after finishing repair jobs to the Singer's jacket, is to weave the future onto the blank space on the jacket's shoulders, just as Thomas will carve the future onto the staff and Jo will sing it. Note what we are told in the final chapter:
The three of them--the new little Singer who would one day take the chained Singer's place; Thomas the Carver, who with his meticulous tools wrote the history of the world; and she herself, the rone who coloured that history--they were the artists who could create the future.
For the Guardians, then, who are obsessed about maintaining control and preserving their rules in the society that this story is set in, to control the future means to maintain their power. They have found a way "to steal and harness other people's powers for their own needs." Their manipulation and abuse of power is forcing the children to "describe the future they wanted, not the one that could be." So, because of their ability to "create" the future, Jo, Thomas and Kira are incredibly and vitally important, both for the preservation and the future of humanity, but also for the cynical Guardians, who intend to use them to maintain their power.
Kira, Thomas, and Jo have all been taken into the Edifice because all three of them have special talents that the Guardian all believe are useful. Jo is to succeed the Singer, singing the future, whereas Thomas will be the Carver, carving the future onto the staff. Lastly, Kira will be weaving the future onto the Singer's jacket.
The three of them have special talents important to the populace in which they are living.