At the end of the series, some outcasts have become part of the council in King's landing yes, but it feels quite incomplete.
I liked the council scene, seeing the "sidekicks" of some of the main players come together. My read on that was here are the actual people doing the work of running the kingdom while the ruling family class squabble and war. The "true power", at least as it manifests day to day for the people of Westeros, was actually around the table in the hands of (mostly) well meaning, hard working individuals.
Note: I know Tyrion is a Lannister and part of the ruling class, but the Lannisters are pretty much neutered at this point.