Originally Posted by
Grunty
The mission was also likely secret, so it's not that the population would know of what he did yet and lost for the mission.
However from what we can see so far, i'm not sure reputation or even leading ability are the main reason for someone being chosen for the council, which is a sham anyway.
The main qualities as far as i can see it are nepotism (Storm, Emma, Kitty, Jean, Nightcrawler) and realpolitik (Apocalypse, Exodus, Mystique, Shaw, Sinister), with Xavier and Magneto being there because they are the de-facto leaders anyway and Krakoa because... well obvious.
Though with that in mind Everett could make it to the Council, but only if either of the above reasons is big enough for him to be thrown in.